PSE 9e Ch 24 Ch 25 26 Combined Serway

7/25/2019 PSE 9e Ch 24 Ch 25 26 Combined Serway

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Chapter 24—Gauss's Law

MULTIPLE CHOICE

1. Two charges of 15 pC and −40 pC are inside a cube with sides that are of 0.40-m length. Determine the

net electric flux through the surface of the cube.

a. +.! " ×m

#C b. −1.1 " ×m#C

c. +1.1 " ×m#C

d. −.! " ×m#C

e. −0.4$ " ×m#C

%"&' D (T&' D)*' %erage

. The total electric flux through a closed c,lindrical length 1. m/ diameter 0.0 m surface is eual

to −5.0 " ×m#C. Determine the net charge within the c,linder.

a. −2 pC

b. −53 pC

c. −44 pC

d. −$1 pC

e. −12 pC

%"&' C (T&' D)*' %erage

3. Charges q and Q are placed on the x axis at x 0 and x .0 m/ respectiel,. )f q −40 pC and Q

+30 pC/ determine the net flux through a spherical surface radius 1.0 m centered on the origin.

a. −.2 " ×m#C

b. −2.! " ×m#C

c. −!.5 " ×m#C

d. −4.5 " ×m#Ce. −1.1 " ×m#C

%"&' D (T&' D)*' %erage

4. % uniform linear charge densit, of 4.0 nC#m is distributed along the entire x axis. Consider a spherical

radius 5.0 cm surface centered on the origin. Determine the electric flux through this surface.

a. 2! " ×m#C

b. 2 " ×m#C

c. 45 " ×m#C

d. $ " ×m#C

e. 3 " ×m#C

%"&' C (T&' D)*' %erage

5. % uniform charge densit, of 500 nC#m3 is distributed throughout a spherical olume radius 12 cm.

Consider a cubical 4.0 cm along the edge surface completel, inside the sphere. Determine the

electric flux through this surface.

a. $.1 " ×m#C

b. 3.2 " ×m#C



c. 1 " ×m#C

d. 1 " ×m#C

e. $0 " ×m#C

%"&' (T&' D)*' %erage

2. % point charge +Q is located on the x axis at x a/ and a second point charge −Q is located on the x

axis at x −

a. % 6aussian surface with radius r a is centered at the origin. The flux through this6aussian surface is

a. 7ero because the negatie flux oer one hemisphere is eual to the positie flux oer the

other.

b. greater than 7ero.

c. 7ero because at eer, point on the surface the electric field has no component

perpendicular to the surface.

d. 7ero because the electric field is 7ero at eer, point on the surface.

e. none of the aboe.

%"&' % (T&' 1 D)*' 8as,

$. The xy plane is 9painted9 with a uniform surface charge densit, which is eual to 40 nC#m. Consider a

spherical surface with a 4.0-cm radius that has a point in the xy plane as its center. :hat is the electricflux through that part of the spherical surface for which z ; 0<

a. 14 " ×m#C

b. 11 " ×m#C

c. 1$ " ×m#C

d. 0 " ×m#C

e. 3 " ×m#C

%"&' (T&' D)*' %erage

!. % long c,linder radius 3.0 cm is filled with a nonconducting material which carries a uniform

charge densit, of 1.3 µ C#m

3

. Determine the electric flux through a spherical surface radius .0 cmwhich has a point on the axis of the c,linder as its center.

a. 5.$ " ×m#C

b. 4. " ×m#C

c. 2.4 " ×m#C

d. $. " ×m#C

e. 15 " ×m#C

%"&' (T&' D)*' %erage

. Charge of uniform surface densit, 4.0 nC#m is distributed on a spherical surface radius .0 cm.

:hat is the total electric flux through a concentric spherical surface with a radius of 4.0 cm<

a. .! " ×m#C b. 1.$ " ×m#C

c. .3 " ×m#C

d. 4.0 " ×m#C

e. .1 " ×m#C

%"&' C (T&' D)*' %erage



10. % charge of uniform olume densit, 40 nC#m3 fills a cube with !.0-cm edges. :hat is the total

electric flux through the surface of this cube<

a. . " ×m#C

b. .0 " ×m#C

c. .2 " ×m#C

d. .3 " ×m#C

e. 1.! " ×m#C

%"&' D (T&' D)*' %erage

11. % charge of 0.!0 nC is placed at the center of a cube that measures 4.0 m along each edge. :hat is the

electric flux through one face of the cube<

a. 0 " ×m#C

b. 15 " ×m#C

c. 45 " ×m#C

d. 3 " ×m#C

e. 24 " ×m#C

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1. % hemispherical surface half of a spherical surface of radius R is located in a uniform electric field of

magnitude E that is parallel to the axis of the hemisphere. :hat is the magnitude of the electric flux

through the hemisphere surface<a. π R E

b. 4π R E #3

c. π R E #3

d. π R E #

e. π R E #3

%"&' % (T&' 1 D)*' 8as,

13. The electric field in the region of space shown is gien b, "#C where y is in m. :hat is

the magnitude of the electric flux through the top face of the cube shown<

a. 0 " ×m#C

b. 2.0 " ×m#C

c. 54 " ×m#C

d. 1 " ×m#C



e. 12 " ×m#C

%"&' C (T&' D)*' %erage

14. Charge of uniform surface densit, 0.0 nC#m is distributed oer the entire xy plane. Determine the

magnitude of the electric field at an, point haing z .0 m.

a. 1$ "#C

b. 11 "#C

c. 3 "#Cd. ! "#C

e. 40 "#C

%"&' (T&' D)*' %erage

15. Two infinite parallel surfaces carr, uniform charge densities of 0.0 nC#m and −0.20 nC#m. :hat is

the magnitude of the electric field at a point between the two surfaces<

a. 34 "#C

b. 3 "#C

c. 45 "#Cd. 1$ "#C

e. 0 "#C

%"&' C (T&' D)*' %erage

12. Two infinite/ uniforml, charged/ flat surfaces are mutuall, perpendicular. =ne of the sheets has a

charge densit, of +20 pC#m/ and the other carries a charge densit, of −!0 pC#m. :hat is the

magnitude of the electric field at an, point not on either surface<

a. 1.1 "#C

b. 5.2 "#C

c. $. "#C

d. 3.! "#C

e. 4.0 "#C

%"&' (T&' D)*' %erage

1$. Charge of a uniform densit, !.0 nC#m is distributed oer the entire xy plane. % charge of uniform

densit, 3.0 nC#m is distributed oer the parallel plane defined b, z .0 m. Determine the

magnitude of the electric field for an, point with z 3.0 m.

a. 0.$ >"#C

b. 0.1$ >"#C

c. 0.2 >"#C

d. 0.34 >"#C

e. 0.! >"#C

%"&' C (T&' D)*' %erage

1!. Charge of a uniform densit, !.0 nC#m is distributed oer the entire xy plane. % charge of uniform

densit, 5.0 nC#m is distributed oer the parallel plane defined b, z .0 m. Determine the

magnitude of the electric field for an, point with z 1.0 m.

a. 0.45 >"#C

b. 0.1$ >"#C

c. 0.! >"#C

d. 0.$3 >"#C

e. 0.2 >"#C



%"&' (T&' D)*' %erage

1. Charge of uniform densit, 0.30 nC#m is distributed oer the xy plane/ and charge of uniform densit,

−0.40 nC#m is distributed oer the yz plane. :hat is the magnitude of the resulting electric field at

an, point not in either of the two charged planes<a. 40 "#C

b. 34 "#C

c. ! "#Cd. 42 "#Ce. 2.0 "#C

%"&' C (T&' D)*' %erage

0. % long nonconducting c,linder radius 1 cm has a charge of uniform densit, 5.0 nC#m3

distributed throughout its column. Determine the magnitude of the electric field 5.0 cm from the axis

of the c,linder.

a. 5 "#C

b. 0 "#C

c. 14 "#C

d. 31 "#Ce. 34 "#C

%"&' C (T&' D)*' %erage

1. % long nonconducting c,linder radius 1 cm has a charge of uniform densit, 5.0 nC#m3

distributed throughout its olume. Determine the magnitude of the electric field 15 cm from the axis of

the c,linder.

a. 0 "#C

b. $ "#C

c. 12 "#C

d. 1 "#C

e. 54 "#C

%"&' (T&' D)*' %erage

. 8ach .0-m length of a long c,linder radius 4.0 mm has a charge of 4.0 nC distributed uniforml,

throughout its olume. :hat is the magnitude of the electric field at a point 5.0 mm from the axis of

the c,linder<

a. . >"#C

b. !.1 >"#C

c. .0 >"#C

d. $. >"#C

e. 1! >"#C

%"&' D (T&' D)*' %erage

3. % long nonconducting c,linder radius 2.0 mm has a nonuniform olume charge densit, gien b,

α r / where α 2. mC#m5 and r is the distance from the axis of the c,linder. :hat is the magnitude of

the electric field at a point .0 mm from the axis<a. 1.4 "#C

b. 1.2 "#C

c. 1.! "#C

d. .0 "#C



e. 5.4 "#C

%"&' % (T&' 3 D)*' Challenging

4. % long c,lindrical shell radius .0 cm has a charge uniforml, distributed on its surface. )f the

magnitude of the electric field at a point !.0 cm radiall, outward from the axis of the shell is !5 "#C/

how much charge is distributed on a .0-m length of the charged c,lindrical surface<

a. 0.3! nC

b. 0.$2 nCc. 0.1 nC

d. 0.5$ nC

e. 0.! nC

%"&' (T&' D)*' %erage

5. Charge of uniform linear densit, 4.0 nC#m is distributed along the entire x axis. Determine the

magnitude of the electric field on the y axis at y .5 m.a. 32 "#C

b. "#C

c. 43 "#C

d. 50 "#Ce. 5! "#C

%"&' (T&' D)*' %erage

2. Charge of uniform densit, !0 nC#m3 is distributed throughout a hollow c,lindrical region formed b,

two coaxial c,lindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric

field at a point which is .0 mm from the s,mmetr, axis.

a. $. "#C

b. .0 "#Cc. 5. "#C

d. 2.! "#C

e. 1! "#C

%"&' D (T&' 3 D)*' Challenging

$. Charge of uniform densit, !0 nC#m3 is distributed throughout a hollow c,lindrical region formed b,

two coaxial c,lindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric

field at a point which is 4.0 mm from the s,mmetr, axis.

a. $. "#C

b. 10 "#C

c. .0 "#C

d. !. "#Ce. 1$ "#C

%"&' C (T&' 3 D)*' Challenging

!. Charge of uniform densit, 0 nC#m is distributed oer a c,lindrical surface radius 1.0 cm/ and a

second coaxial surface radius 3.0 cm carries a uniform charge densit, of −1 nC#m. Determine the

magnitude of the electric field at a point .0 cm from the s,mmetr, axis of the two surfaces.

a. .3 >"#C

b. 1.1 >"#C

c. 1.$ >"#C

d. 3.4 >"#C



e. 4.5 >"#C

%"&' (T&' 3 D)*' Challenging

. Charge of uniform densit, 0 nC#m is distributed oer a c,lindrical surface radius 1.0 cm/ and a

second coaxial surface radius 3.0 cm carries a uniform charge densit, of −1 nC#m. Determine the

magnitude of the electric field at a point 4.0 cm from the s,mmetr, axis of the two surfaces.

a. 0.45 >"#C

b. 1.0 >"#Cc. 0.$3 >"#C

d. 0.52 >"#C

e. .3 >"#C


30. Charge of uniform densit, 40 pC#m is distributed on a spherical surface radius 1.0 cm/ and a

second concentric spherical surface radius 3.0 cm carries a uniform charge densit, of 20 pC#m .

:hat is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces<

a. 3.! "#C b. 4.1 "#C

c. 3.5 "#Cd. 3. "#C

e. 0.! "#C


31. % solid nonconducting sphere radius 1 cm has a charge of uniform densit, 30 nC#m3 distributed

throughout its olume. Determine the magnitude of the electric field 15 cm from the center of the

sphere.

a. "#C

b. 4 "#C

c. 31 "#Cd. !$ "#C

e. 2 "#C

%"&' D (T&' D)*' %erage

3. % 5.0-nC point charge is embedded at the center of a nonconducting sphere radius .0 cm which

has a charge of −!.0 nC distributed uniforml, throughout its olume. :hat is the magnitude of the

electric field at a point that is 1.0 cm from the center of the sphere<

a. 1.! × 105 "#C

b. .0 × 104 "#C

c. 3.2 × 105 "#C

d. .$ × 105 "#C

e. $.×

10

5

"#C

%"&' C (T&' D)*' %erage

33. % charge of 5.0 pC is distributed uniforml, on a spherical surface radius .0 cm/ and a second

charge of −.0 pC is distributed uniforml, on a concentric spherical surface radius 4.0 cm.

Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces.

a. 30 "#C

b. 50 "#C



c. 40 "#C

d. 0 "#C

e. $0 "#C

%"&' (T&' D)*' %erage

34. % charge of !.0 pC is distributed uniforml, on a spherical surface radius .0 cm/ and a second

charge of −3.0 pC is distributed uniforml, on a concentric spherical surface radius 4.0 cm.

Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces.a. 14 "#C

b. 11 "#C

c. "#C

d. 1! "#C

e. 40 "#C

%"&' D (T&' D)*' %erage

35. % point charge 5.0 pC is located at the center of a spherical surface radius .0 cm/ and a charge of

3.0 pC is spread uniforml, upon this surface. Determine the magnitude of the electric field 1.0 cmfrom the point charge.

a. 0.$ >"#C b. 0.45 >"#C

c. 0.23 >"#C

d. 0.0 >"#C

e. 0.1! >"#C

%"&' (T&' D)*' %erage

32. Charge of uniform densit, 40 pC#m is distributed on a spherical surface radius 1.0 cm/ and a

second concentric spherical surface radius 3.0 cm carries a uniform charge densit, of 20 pC#m .

:hat is the magnitude of the electric field at a point .0 cm from the center of the two surfaces<

a. 1.1 "#C b. 4.5 "#C

c. 1.4 "#C

d. 5.2 "#C

e. 0.50 "#C

%"&' % (T&' D)*' %erage

3$. % 4.0-pC point charge is placed at the center of a hollow inner radius .0 cm/ outer radius 4.0 cm

conducting sphere which has a net charge of 4.0 pC. Determine the magnitude of the electric field at a

point which is 2.0 cm from the point charge.

a. 35 "#C

b. 5 "#C

c. 30 "#C

d. 0 "#Ce. 10 "#C

%"&' D (T&' D)*' %erage

3!. The axis of a long hollow metallic c,linder inner radius 1.0 cm/ outer radius .0 cm coincides

with a long wire. The wire has a linear charge densit, of −!.0 pC#m/ and the c,linder has a net charge

per unit length of −4.0 pC#m. Determine the magnitude of the electric field 3.0 cm from the axis.

a. 5.4 "#C



b. $. "#C

c. 4.3 "#C

d. 3.2 "#C

e. .4 "#C

%"&' (T&' D)*' %erage

3. % long straight metal rod has a radius of .0 mm and a surface charge of densit, 0.40 nC#m.

Determine the magnitude of the electric field 3.0 mm from the axis.a. 1! "#C

b. 3 "#C

c. 30 "#C

d. 15 "#C

e. 20 "#C

%"&' C (T&' D)*' %erage

40. )f the electric field ?ust outside a thin conducting sheet is eual to 1.5 "#C/ determine the surface

charge densit, on the conductor.

a. 53 pC#m

b. $ pC#m

c. 35 pC#m

d. 13 pC#m

e. 2.2 pC#m

%"&' D (T&' D)*' %erage

41. The field ?ust outside the surface of a long conducting c,linder which has a .0-cm radius points

radiall, outward and has a magnitude of 00 "#C. :hat is the charge densit, on the surface of the

c,linder<a. .$ nC#m

b. 1.! nC#m

c. 3.5 nC#m

d. 4.4 nC#m

e. 0.0 nC#m

%"&' (T&' D)*' %erage

4. % spherical conductor radius 1.0 cm with a charge of .0 pC is within a concentric hollow spherical

conductor inner radius 3.0 cm/ outer radius 4.0 cm which has a total charge of −3.0 pC. :hat is

the magnitude of the electric field .0 cm from the center of these conductors<

a. 3 "#C

b. 7ero

c. 45 "#C

d. 0 "#C

e. 110 "#C

%"&' C (T&' D)*' %erage

43. % long c,lindrical conductor radius 1.0 mm carries a charge densit, of 4.0 pC#m and is inside a

coaxial/ hollow/ c,lindrical conductor inner radius 3.0 mm/ outer radius 4.0 mm that has a total

charge of −!.0 pC#m. :hat is the magnitude of the electric field .0 mm from the axis of these

conductors<

a. 4 "#C



b. 1! "#C

c. 7ero

d. 32 "#C

e. 2 "#C

%"&' D (T&' D)*' %erage

44. The electric field ?ust outside the surface of a hollow conducting sphere of radius 0 cm has a

magnitude of 500 "#C and is directed outward. %n un>nown charge Q is introduced into the center ofthe sphere and it is noted that the electric field is still directed outward but has decreased to 100 "#C.

:hat is the magnitude of the charge Q<

a. 1.5 nC

b. 1.! nC

c. 1.3 nC

d. 1.1 nC

e. .$ nC

%"&' (T&' D)*' %erage

45. % point charge of 2.0 nC is placed at the center of a hollow spherical conductor inner radius 1.0 cm/

outer radius .0 cm which has a net charge of−

4.0 nC. Determine the resulting charge densit, onthe inner surface of the conducting sphere.

a. +4.! µ C#m

b. −4.! µ C#m

c. −.5 µ C#m

d. +.5 µ C#m

e. −!.0 µ C#m

%"&' (T&' D)*' %erage

42. %n astronaut is in an all-metal chamber outside the space station when a solar storm results in the

deposit of a large positie charge on the station. :hich statement is correct<

a. The astronaut must abandon the chamber immediatel, to aoid being electrocuted. b. The astronaut will be safe onl, if she is wearing a spacesuit made of non-conducting

materials.

c. The astronaut does not need to worr,' the charge will remain on the outside surface.

d. The astronaut must abandon the chamber if the electric field on the outside surface

becomes greater than the brea>down field of air.e. The astronaut must abandon the chamber immediatel, because the electric field inside the

chamber is non-uniform.

%"&' C (T&' 1 D)*' 8as,

4$. % small metal sphere is suspended from the conducting coer of a conducting metal ice buc>et b, a

non-conducting thread. The sphere is gien a negatie charge before the coer is placed on the buc>et.The buc>et is tilted b, means of a non-conducting material so that the charged sphere touches the

inside of the buc>et. :hich statement is correct<

a. The negatie charge remains on the metal sphere.

b. The negatie charge spreads oer the outside surface of the buc>et and coer.

c. The negatie charge spreads oer the inside surface of the buc>et and coer.

d. The negatie charge spreads euall, oer the inside and outside surfaces of the buc>et andcoer.

e. The negatie charge spreads euall, oer the sphere and the inside and outside surfaces of



the buc>et and coer.

%"&' (T&' 1 D)*' 8as,

4!. % positie point charge q is placed off center inside an uncharged metal sphere insulated from the

ground as shown. :here is the induced charge densit, greatest in magnitude and what is its sign<

a. %@ negatie.

b. %@ positie.c. @ negatie.

d. @ positie.

e. C@ negatie.

%"&' % (T&' 1 D)*' 8as,

4. % positie point charge q is placed at the center of an uncharged metal sphere insulated from the

ground. The outside of the sphere is then grounded as shown. Then the ground wire is remoed. % is

the inner surface and is the outer surface. :hich statement is correct<

a. The charge on % is−

q@ that on is +q. b. The charge on is −q@ that on % is +q.

c.

The charge is on % and on .

d. There is no charge on either % or .

e. The charge on % is −q@ there is no charge on .

%"&' 8 (T&' 1 D)*' 8as,

50. %n uncharged metal sphere is placed on an insulating puc> on a frictionless table. :hile being held

parallel to the table/ a rod with a charge q is brought close to the sphere/ but does not touch it. %s the

rod is brought in/ the sphere

a. remains at rest. b. moes toward the rod.

c. moes awa, from the rod.

d. moes perpendicular to the elocit, ector of the rod.

e. moes upward off the puc>.

%"&' (T&' 1 D)*' 8as,



51. Three originall, uncharged infinite parallel planes are arranged as shown. Then the upper plate has

surface charge densit, σ placed on it while the lower plate receies surface charge densit, −σ . The net

charge induced on the center plate is

a. 0.

b. −σ #.

c. +σ #.

d. −σ .

e. +σ .

%"&' % (T&' 1 D)*' 8as,

5. Two concentric imaginar, spherical surfaces of radius R and R respectiel, surround a positie point

charge Q located at the center of the surfaces. :hen compared to the electric flux Φ1 through the

surface of radius R/ the electric flux Φ through the surface of radius R is

a.

.

b.

.

c. Φ Φ1.

d. Φ Φ1.

e. Φ 4Φ1.

%"&' C (T&' 1 D)*' 8as,

53. Two concentric imaginar, spherical surfaces of radius R and R respectiel, surround a positie point

charge −Q located at the center of the surfaces. :hen compared to the electric flux Φ1 through the

surface of radius R/ the electric flux Φ through the surface of radius R is

a.

.

b.

.

c. Φ Φ1.

d. Φ Φ1.

e. Φ 4Φ1.

%"&' C (T&' 1 D)*' 8as,

54. :hen a cube is inscribed in a sphere of radius r / the length L of a side of the cube is . )f a

positie point charge Q is placed at the center of the spherical surface/ the ratio of the electric flux

Φ sphere at the spherical surface to the flux Φcube at the surface of the cube is



a.

.

b.

.

c. 1.

d.

.e.

.

%"&' C (T&' 1 D)*' 8as,

55. The electric flux through the two ad?acent spherical surfaces shown below is >nown to be the same.

)t is also >nown that there is no charge inside either spherical surface. :e can conclude thata. there is no electric field present in this region of space.

b. there is a constant 8 field present in this region of space.

c. the electric flux has a constant alue of 7ero.d. an, of the aboe ma, be correct.

e. onl, a and b aboe ma, be correct.

%"&' D (T&' 1 D)*' 8as,

52. :hich one of the following cannot be a statement of 6aussAs Baw for some ph,sical situation<

a. 4π r ε 0 E Q.

b. π rLε 0 E Q.

c..

d..

e..

%"&' D (T&' 1 D)*' 8as,

5$. :hich one of the following is not an expression for electric charge<

a.

b.

c.

d.



e.

%"&' D (T&' 1 D)*' 8as,

5!. %n uncharged spherical conducting shell surrounds a charge −q at the center of the shell. The charges

on the inner and outer surfaces of the shell are respectiel,

a. −q/ −q. b. −q/ +q.

c. +q/ −q.

d. +q/ +q.

e. +q/ 0.

%"&' C (T&' 1 D)*' 8as,

5. %n uncharged spherical conducting shell surrounds a charge −q at the center of the shell. Then charge

+3q is placed on the outside of the shell. :hen static euilibrium is reached/ the charges on the inner

and outer surfaces of the shell are respectiel,

a. +q/ −q.

b. −q/ +q.c. +q/ +q.

d. +2q/ +q.

e. +3q/ 0.

%"&' C (T&' 1 D)*' 8as,

20. % constant electric field is present throughout a region of space that includes the plane

bounded b, the x and y axes and the lines x 30 cm and y 50 cm. The electric flux through the

planeAs surface/ in " ×m#C/ is

a. 0.

b. 0.5.c. 5.

d. 50.

e. 100.

%"&' % (T&' 1 D)*' 8as,

21. % constant electric field is present throughout a region of space that includes the plane

bounded b, the y and z axes and the lines y 50 cm and z 50 cm. The electric flux through the

planeAs surface/ in " ×m#C/ is

a. 0.

b. 0.5.c. 5.

d. 50.e. 100.

%"&' C (T&' D)*' %erage



2. % spaceship encounters a single plane of charged particles/ with the charge per unit area eual to σ .

The electric field a short distance aboe the plane has magnitude and is directed to the

plane.

a.

/ parallel b.

/ perpendicular c.

/ parallel

d.

/ perpendicular

e.

/ parallel

%"&' (T&' 1 D)*' 8as,

23. ou are told that summed oer both the surface areas of sphere % and sphere below totals

to . ou can conclude that

a. &phere % contains charge qin −Q.

b. &phere contains charge qin −Q.c. &phere contains charge qin +Q.

d.

8ach sphere contains charge .

e. The sum of the charges contained in both spheres is −Q.

%"&' 8 (T&' 1 D)*' 8as,

24. )f we define the graitational field / where is a unit radial ector/ then 6aussAs Baw

for grait, is

a..

b..

c..

d..



e..

%"&' C (T&' D)*' %erage

25. 6ino sa,s that the analog of 6aussAs law for the flow of an incompressible fluid of densit, ρ at

constant elocit, is for an imaginar, surface within the fluid. Boren7o sa,s that it is

true onl, if the area where the fluid enters the surface and the area where it leaes the surface are both perpendicular to the elocit, of the fluid. :hich one/ if either/ is correct<a. 6ino/ because as much fluid leaes as enters.

b.Boren7o/ because is not eual to 7ero if the fluid enters or exits at angles other

than 0°.

c. Boren7o/ because this is true onl, when the fluid executes rotational motion.

d. 6ino/ because it is true onl, when the fluid is enclosed on all sides/ not when it is flowing.

e. Boren7o/ because it is true onl, when the fluid is enclosed on all sides/ not when it is

flowing.

%"&' % (T&' 1 D)*' 8as,

22. % beam of electrons moes at elocit, . The number of particles per unit olume in the beam of

area A is ρ . )f we imagine a c,lindrical 6aussian surface of radius r and length centered on the beam/

the electron flux through the surface is

a. 0.

b. ρ v f A.

c. 2 ρ v f A.

d. ρ v f A+π r .

e. 2ρ v f A+π r .

%"&' % (T&' 1 D)*' 8as,

2$. % student has made the statement that the electric flux through one half of a 6aussian surface is alwa,seual and opposite to the flux through the other half of the 6aussian surface. This is

a. neer true.

b. neer false.

c. true wheneer enclosed charge is s,mmetricall, located at a center point/ or on a center

line or centrall, placed plane.

d. true wheneer no charge is enclosed within the 6aussian surface.

e. true onl, when no charge is enclosed within the 6aussian surface.

%"&' 8 (T&' 1 D)*' 8as,

2!. % student has made the statement that the electric flux through one half of a 6aussian surface is alwa,s

eual to the flux through the other half of the 6aussian surface. This isa. neer true.

b. neer false.c. true wheneer enclosed charge is s,mmetricall, located at a center point/ on a center line/

or on a centrall, placed plane.

d. true wheneer no charge is enclosed within the 6aussian surface.

e. true onl, when no charge is enclosed within the 6aussian surface.

%"&' C (T&' 1 D)*' 8as,



2. Two planes of charge with no thic>ness/ % and / are parallel and ertical. The electric field in the

region between the two planes has magnitude . The electric field in the region to the left of % and

the electric field in the region to the right of ma, hae the magnitudes

a. 0/ 0.

b.

/ .

c.

/ .

d. gien in an, answer aboe.

e. gien onl, in answer a or b aboe.

%"&' D (T&' D)*' %erage

$0. Two planes of charge with no thic>ness/ % and / are parallel and ertical. The electric field in region )

to the left of plane % has magnitude and points to the left. The electric field in the region to the

right of has magnitude and points to the right. The electric field in the region between the two

planes has magnitude and points to the right. The surface charge densit, on planes % and

respectiel, is

a.

/ σ .

b.

/ σ.

c.

σ / .

d.

σ / .

e. σ / σ .

%"&' 8 (T&' D)*' %erage

$1. :hitne, sa,s that 6aussAs Baw can be used to find the electric field of a sufficientl, s,mmetrical

distribution of charge as long as oer the whole 6aussian surface. %lgie sa,s that the

electric field must be a constant ector oer the entire 6aussian surface. :hich one/ if either/ is

correct<

a. :hitne,/ because that means no charge is enclosed within the 6aussian surface. b.

%lgie/ because a constant electric field means that .

c. oth/ because the conditions in a and b are euialent.

d. "either/ because the electric field can be found from 6aussAs law onl, if holds

onl, oer a portion of the 6aussian surface.

e. "either/ because the charge distribution must be s,mmetric if an,where on the

surface.



%"&' D (T&' D)*' %erage

$. % uniform electric field is present in the region between the infinite parallel planes of charge % and

/ and a uniform electric field is present in the region between the infinite parallel planes of charge

and C. :hen the planes are ertical and the fields are both non-7ero/a.

and are both directed to the right. b.

and are both directed to the left.c.

points to the right and to the left.

d. points to the left and to the right.

e. %n, one of the aboe is possible.

%"&' 8 (T&' 1 D)*' 8as,

$3. % uniform electric field is present in the region between infinite parallel plane plates % and and a

uniform electric field is present in the region between infinite parallel plane plates and C. :hen

the plates are ertical/ is directed to the right and to the left. The signs of the charges on plates

%/ and C ma, be

a. −/ −/ −.

b. +/ −/ −.

c. +/ −/ +.

d. +/ +/ +.

e. an, one of the aboe.

%"&' 8 (T&' 1 D)*' 8as,

$4. Three infinite planes of charge/ %/ and C/ are ertical and parallel to one another. There is a uniform

electric field to the left of plane % and a uniform electric field to the right of plane C. The field

points to the left and the field points to the right. The signs of the charges on plates %/ and C

ma, bea. −/ −/ −.

b. +/ −/ −.

c. +/ −/ +.

d. +/ +/ +.

e. an, one of the aboe.

%"&' 8 (T&' 1 D)*' 8as,

$5. %n constant electric field/ "#C/ goes through a surface with area m. This

surface can also be expressed as an area of 10 m with the direction of the unit ector .

:hat is the magnitude of the electric flux through this area<

a. 4 " ×m#C

b. 4! " ×m#C

c. 0.4 " ×m#C

d. 0.4! " ×m#C



e. 0

%"&' % (T&' D)*' %erage

$2. % point charge is located at the origin. Centered along the x axis is a c,lindrical closed surface of

radius 10 cm with one end surface located at x m and the other end surface located at x 4 m. )f

the magnitude of the electric flux through the surface at x m is 4 " ×m#C/ what is the magnitude

of the electric flux through the surface at x 4 m<

a. 1 " ×m#C b. " ×m#C

c. 4 " ×m#C

d. 12 " ×m#C

e. The correct alue is not gien.

%"&' % (T&' D)*' %erage

PROBLEM

$$. The nucleus of lead-0!/ / has ! protons within a sphere of radius 2.34×

10

−15

. 8ach electriccharge has a alue of 1.20 × 10−1 C. %ssuming that the protons create a sphericall, s,mmetric

distribution of charge/ calculate the electric field at the surface of the nucleus.

%"&'

.4 × 101 "#C

(T&' D)*' %erage

$!. %t the point of fission/ a nucleus of E-3!/ with protons is diided into two smaller spheres each

with 42 protons and a radius of 5. × 10−15 m. :hat is the repulsie force pushing the two spheres apart

when the, are ?ust touching one another< The mass of the E-3! nucleus is 3.! × 10−5 >g.

%"&'

3 500 "

(T&' D)*' %erage

$. The nucleus of a h,drogen atom/ a proton/ sets up an electric field. The distance between the proton

and electron is about 5.1 × 10−11 m. :hat is the magnitude of the electric field at this distance from the

proton< FThe charge on the proton is +1.2 × 10−1 C.G

%"&'

5.5 × 1011 "#C

(T&' D)*' %erage

!0. % 6eiger counter is li>e an electroscope that discharges wheneer ions formed b, a radioactie particle

produce a conducting path. % t,pical 6eiger counter consists of a thin conducting wire of radius 0.00

cm stretched along the axis of a conducting c,linder of radius .0 cm. The wire and the c,linder carr,

eual and opposites charges of !.0 × 10−10 C all along their length of 10.0 cm. :hat is the magnitude

of the electric field at the surface of the wire<



%"&'

$. × 102 "#C

(T&' D)*' %erage

Chapter 25—Electric Pte!tial

MULTIPLE CHOICE

1. % charged particle q −!.0 mC/ which moes in a region where the onl, force acting on the particle

is an electric force/ is released from rest at point %. %t point the >inetic energ, of the particle is

eual to 4.! H. :hat is the electric potential difference V − V %<

a. −0.20 >I

b. +0.20 >I

c. +0.!0 >I

d. −0.!0 >I

e. +0.4! >I

%"&' (T&' D)*' %erage

. % particle charge 50 µ C moes in a region where the onl, force on it is an electric force. %s the

particle moes 5 cm from point % to point / its >inetic energ, increases b, 1.5 mH. Determine the

electric potential difference/ V − V %.

a. −50 I

b. −40 I

c. −30 I

d. −20 I

e. +15 I

%"&' C (T&' D)*' %erage

3. (oints % Fat / 3 mG and Fat 5/ $ mG are in a region where the electric field is uniform and gien

b, "#C. :hat is the potential difference V % − V <

a. 33 I

b. $ Ic. 30 I

d. 4 I

e. 11 I

%"&' D (T&' D)*' %erage

4. % particle charge +.0 mC moing in a region where onl, electric forces act on it has a >inetic

energ, of 5.0 H at point %. The particle subseuentl, passes through point which has an electric

potential of +1.5 >I relatie to point %. Determine the >inetic energ, of the particle as it moes

through point .

a. 3.0 H

b. .0 H

c. 5.0 Hd. !.0 H



e. 10.0 H

%"&' (T&' D)*' %erage

5. % particle mass 2.$ × 10−$ >g/ charge 3. × 10−1 C moes along the positie x axis with a speed

of 4.! × 105 m#s. )t enters a region of uniform electric field parallel to its motion and comes to rest after

moing .0 m into the field. :hat is the magnitude of the electric field<

a. .0 >"#C

b. 1.5 >"#Cc. 1. >"#C

d. 3.5 >"#C

e. .4 >"#C

%"&' C (T&' D)*' %erage

2. % proton mass 1.2$ × 10−$ >g/ charge 1.20 × 10−1 C moes from point % to point under the

influence of an electrostatic force onl,. %t point % the proton moes with a speed of 50 >m#s. %t point

the speed of the proton is !0 >m#s. Determine the potential difference V − V %.

a. +0 I

b. −0 I

c. −$ I

d. +$ I

e. −40 I

%"&' (T&' D)*' %erage

$. % proton mass 1.2$ × 10−$ >g/ charge 1.20 × 10−1 C moes from point % to point under the

influence of an electrostatic force onl,. %t point % the proton moes with a speed of 20 >m#s. %t point

the speed of the proton is !0 >m#s. Determine the potential difference V − V %.

a. +15 I

b. −15 I

c. −33 Id. +33 I

e. −0 I

%"&' (T&' D)*' %erage

!. :hat is the speed of a proton that has been accelerated from rest through a potential difference of 4.0

>I<a. 1.1 × 102 m#s

b. .! × 105 m#s

c. !.! × 105 m#s

d. 1. × 102 m#s

e. 2. × 105 m#s

%"&' C (T&' D)*' %erage

. %n electron m .1 × 10−31 >g/ q −1.2 × 10−1 C starts from rest at point % and has a speed of 5.0 ×

102 m#s at point . =nl, electric forces act on it during this motion. Determine the electric potential

difference V % − V .

a. −$1 I

b. +$1 I



c. −2 I

d. +2 I

e. −140 I

%"&' % (T&' D)*' %erage

10. % proton m 1.$ × 10−$ >g/ q +1.2 × 10−1 C starts from rest at point % and has a speed of 40 >m#s

at point . =nl, electric forces act on it during this motion. Determine the electric potential difference

V − V %.

a. +!.5 I

b. −!.5 I

c. −4.! I

d. +4.! I

e. −1$ I

%"&' (T&' D)*' %erage

11. % particle m .0 µ g/ q −5.0 µ C has a speed of 30 m#s at point % and moes with onl, electric

forces acting on it to point where its speed is !0 m#s. Determine the electric potential difference V %

− V

.

a. −. >I

b. +1.1 >I

c. −1.1 >I

d. +. >I

e. +1.3 >I

%"&' C (T&' D)*' %erage

1. %n alpha particle m 2.$ × 10−$ >g/ q +3. × 10−1 C has a speed of 0 >m#s at point % and moes

to point where it momentaril, stops. =nl, electric forces act on the particle during this motion.

Determine the electric potential difference V % − V .

a. +4. I b. −4. I

c. −.4 I

d. +.4 I

e. −!.4 I

%"&' (T&' D)*' %erage

13. (oints % Fat 3/ 2 mG and Fat !/ −3 mG are in a region where the electric field is uniform and gien

b, "#C. :hat is the electric potential difference V % − V <

a. +20 I

b. −20 I

c. +!0 I

d. −!0 I

e. +50 I

%"&' % (T&' D)*' %erage

14. )f a 30 cm/ b 0 cm/ q +.0 nC/ and Q −3.0 nC in the figure/ what is the potential difference V %

− V <



a. +20 I

b. +$ I

c. +!4 I

d. +2 Ie. +4! I

%"&' % (T&' D)*' %erage

15. &eeral charges in the neighborhood of point ( produce an electric potential of 2.0 >I relatie to 7ero

at infinit, and an electric field of "#C at point (. Determine the wor> reuired of an external agent

to moe a 3.0- µ C charge along the x axis from infinit, to point ( without an, net change in the >inetic

energ, of the particle.

a. 1 mH

b. 1! mHc. 4 mH

d. $ mHe. 1 mH

%"&' (T&' D)*' %erage

12. (oint charges q and Q are positioned as shown. )f q +.0 nC/ Q −.0 nC/ a 3.0 m/ and b 4.0 m/

what is the electric potential difference/ V % − V <

a. !.4 I

b. 2.0 I

c. $. I

d. 4.! I

e. 0 I

%"&' D (T&' D)*' %erage

1$. Three charged particles are positioned in the xy plane' a 50-nC charge at y 2 m on the y axis/ a −!0-nC charge at x −4 m on the x axis/ and a $0-nc charge at y −2 m on the y axis. :hat is the electric

potential relatie to a 7ero at infinit, at the point x ! m on the x axis<

a. +!1 I b. +4! I

c. +5.! I

d. −$ I

e. −1! I



%"&' (T&' D)*' %erage

1!. (oint charges of eual magnitudes 5 nC and opposite signs are placed on diagonall, opposite

corners of a 20-cm × !0-cm rectangle. )f point % is the corner of this rectangle nearest the positie

charge and point is located at the intersection of the diagonals of the rectangle/ determine the

potential difference/ V − V %.

a. −4$ I

b. +4 Ic. 7ero

d. −4 I

e. +4$ I

%"&' D (T&' D)*' %erage

1. )dentical .0- µ C charges are located on the ertices of a suare with sides that are .0 m in length.

Determine the electric potential relatie to 7ero at infinit, at the center of the suare.

a. 3! >I

b. 51 >I

c. $2 >I

d. 24 >Ie. 13 >I

%"&' (T&' D)*' %erage

0. % +4.0- µ C charge is placed on the x axis at x +3.0 m/ and a −.0- µ C charge is located on the y axis at

y −1.0 m. (oint % is on the y axis at y +4.0 m. Determine the electric potential at point % relatie

to 7ero at the origin.

a. 2.0 >I

b. !.4 >I

c. .2 >I

d. 4.! >I

e. 3.2 >I

%"&' C (T&' D)*' %erage

1. )dentical 4.0- µ C charges are placed on the y axis at y ±4.0 m. (oint % is on the x axis at x +3.0 m.

Determine the electric potential of point % relatie to 7ero at the origin.a. −4.5 >I

b. −.$ >I

c. −1.! >I

d. −3.2 >I

e. −14 >I

%"&' D (T&' D)*' %erage

. *our identical point charges +2.0 nC are placed at the corners of a rectangle which measures 2.0 m ×

!.0 m. )f the electric potential is ta>en to be 7ero at infinit,/ what is the potential at the geometric

center of this rectangle<

a. 5! I

b. 23 I

c. 43 I

d. !4 I



e. 11 I

%"&' C (T&' D)*' %erage

3. Three identical point charges +.0 nC are placed at the corners of an euilateral triangle with sides of

.0-m length. )f the electric potential is ta>en to be 7ero at infinit,/ what is the potential at the midpoint

of an, one of the sides of the triangle<

a. 12 I

b. 10 Ic. $0 I

d. 42 I

e. 44 I

%"&' D (T&' D)*' %erage

4. % particle charge Q is >ept in a fixed position at point (/ and a second particle charge q is

released from rest when it is a distance R from (. )f Q +.0 mC/ q −1.5 mC/ and R 30 cm/ what is

the >inetic energ, of the moing particle after it has moed a distance of 10 cm<

a. 20 >H b. 45 >H

c. $5 >Hd. 0 >H

e. 30 >H

%"&' (T&' D)*' %erage

5. (article % mass m/ charge Q and mass m/ charge 5 Q are released from rest with the

distance between them eual to 1.0 m. )f Q 1 µ C/ what is the >inetic energ, of particle at the

instant when the particles are 3.0 m apart<

a. !.2 H b. 3.! H

c. 2.0 H

d. . H

e. 4.3 H


2. % particle charge 40 µ C moes directl, toward a second particle charge !0 µ C which is held in

a fixed position. %t an instant when the distance between the two particles is .0 m/ the >inetic energ,

of the moing particle is 12 H. Determine the distance separating the two particles when the moing

particle is momentaril, stopped.

a. 0.$5 m

b. 0.!4 m

c. 0.5 m

d. 0.2! m

e. 0.52 m


$. % particle charge $.5 µ C is released from rest at a point on the x axis/ x 10 cm. )t begins to moe

due to the presence of a .0- µ C charge which remains fixed at the origin. :hat is the >inetic energ, of

the particle at the instant it passes the point x 1.0 m<

a. 3.0 H

b. 1.! H



c. .4 H

d. 1. H

e. 1.4 H

%"&' D (T&' D)*' %erage

!. % particle charge 5.0 µ C is released from rest at a point x 10 cm. )f a 5.0- µ C charge is held fixed

at the origin/ what is the >inetic energ, of the particle after it has moed 0 cm<

a. 1.2 H b. .0 H

c. .4 H

d. 1. H

e. 1.! H

%"&' (T&' D)*' %erage

. % 20- µ C charge is held fixed at the origin and a −0- µ C charge is held fixed on the x axis at a point x

1.0 m. )f a 10- µ C charge is released from rest at a point x 40 cm/ what is its >inetic energ, the instant

it passes the point x $0 cm<a. .! H

b. $.! Hc. !.! H

d. 2. He. .! H

%"&' C (T&' D)*' %erage

30. Two identical particles/ each with a mass of .0 µ g and a charge of 5 nC/ are released simultaneousl,

from rest when the two are 4.0 cm apart. :hat is the speed of either particle at the instant when the

two are separated b, 10 cm<

a. $.3 m#s

b. .! m#s

c. . m#sd. 2.5 m#s

e. 4.2 m#s

%"&' D (T&' D)*' %erage

31. Two particles/ each haing a mass of 3.0 µ g and haing eual but opposite charges of magnitude 5.0

nC/ are released simultaneousl, from rest when the two are 5.0 cm apart. :hat is the speed of either

particle at the instant when the two are separated b, .0 cm<

a. .1 m#s

b. 1.5 m#s

c. 1.! m#s

d. .4 m#s

e. 3. m#s

%"&' (T&' D)*' %erage

3. Two identical particles/ each with a mass of 4.5 µ g and a charge of 30 nC/ are moing directl, toward

each other with eual speeds of 4.0 m#s at an instant when the distance separating the two is eual to

5 cm. Jow far apart will the, be when closest to one another<a. .! cm



b. 1 cm

c. $.! cm

d. 15 cm

e. 0 cm

%"&' C (T&' D)*' %erage

33. Two particles/ each haing a mass of 3.0 µ g and haing eual but opposite charges of magnitude of 2.0

nC/ are released simultaneousl, from rest when the, are a er, large distance apart. :hat distanceseparates the two at the instant when each has a speed of 5.0 m#s<

a. 4.3 mm

b. !.2 mm

c. $.3 mm

d. 5.2 mm

e. . mm

%"&' % (T&' D)*' %erage

34. % particle q +5.0 µ C is released from rest when it is .0 m from a charged particle which is held at

rest. %fter the positiel, charged particle has moed 1.0 m toward the fixed particle/ it has a >inetic

energ, of 50 mH. :hat is the charge on the fixed particle<a. −. µ C

b. +2.$ µ C

c. −.$ µ C

d. +!.0 µ C

e. −1.1 µ C

%"&' % (T&' D)*' %erage

35. *our identical point charges +4.0 µ C are placed at the corners of a suare which has 0-cm sides.

Jow much wor> is reuired to assemble this charge arrangement starting with each of the charges a

er, large distance from an, of the other charges<

a. +. H b. +3. H

c. +. H

d. +4.3 H

e. +1. H


32. )dentical !.0- µ C point charges are positioned on the x axis at x ±1.0 m and released from rest

simultaneousl,. :hat is the >inetic energ, of either of the charges after it has moed .0 m<

a. !4 mH

b. 54 mH

c. 2 mHd. 23 mH

e. 4! mH

%"&' C (T&' D)*' %erage

3$. Through what potential difference must an electron starting from rest be accelerated if it is to reach a

speed of 3.0 × 10$ m#s<

a. 5.! >I



b. .2 >I

c. $.1 >I

d. !.2 >I

e. 5.1 >I

%"&' (T&' D)*' %erage

3!. )dentical point charges +50 µ C are placed at the corners of a suare with sides of .0-m length. Jow

much external energ, is reuired to bring a fifth identical charge from infinit, to the geometric centerof the suare<

a. 41 H

b. 12 H

c. 24 H

d. 10 H

e. !0 H

%"&' C (T&' D)*' %erage

3. % charge of +3.0 µ C is distributed uniforml, along the circumference of a circle with a radius of 0

cm. Jow much external energ, is reuired to bring a charge of 5 µ C from infinit, to the center of the

circle<a. 5.4 H

b. 3.4 Hc. 4.3 H

d. .$ H

e. 2.! H

%"&' (T&' D)*' %erage

40. )dentical point charges +0 µ C are placed at the corners of an euilateral triangle with sides of .0-m

length. Jow much external energ, is reuired to bring a charge of 45 µ C from infinit, to the midpoint

of one side of the triangle<

a. 2 H b. 12 H

c. 3 H

d. 1 H

e. 1 H

%"&' D (T&' D)*' %erage

41. )dentical point charges +30 µ C are placed at the corners of a rectangle 4.0 m × 2.0 m. Jow much

external energ, is reuired to bring a charge of 55 µ C from infinit, to the midpoint of one of the 2.0-m

long sides of the rectangle<

a. H

b. 12 Hc. 13 H

d. 1 H

e. !.0 H

%"&' (T&' D)*' %erage



4. % charge per unit length gien b, λ x bx/ where b 1 nC#m/ is distributed along the x axis from x

+.0 cm to x +12 cm. )f the electric potential at infinit, is ta>en to be 7ero/ what is the electric

potential at the point ( on the y axis at y 1 cm<

a. 5.4 I

b. $. I

c. .0 I

d. . Ie. 12 I


43. % charge Q is uniforml, distributed along the x axis from x a to x b. )f Q 45 nC/ a −3.0 m/ and

b .0 m/ what is the electric potential relatie to 7ero at infinit, at the point/ x !.0 m/ on the x

axis<

a. $1 I

b. 20 I

c. 4 I

d. ! I

e. 150 I


44. Charge of uniform densit, 3.5 nC#m is distributed along the circular arc shown. Determine the

electric potential relatie to 7ero at infinit, at point (.

a. 21 I

b. 4 I

c. 5 I

d. 33 I

e. I

%"&' D (T&' D)*' %erage

45. % charge of uniform densit, 0.!0 nC#m is distributed along the x axis from the origin to the point x

10 cm. :hat is the electric potential relatie to 7ero at infinit, at a point/ x 1! cm/ on the x axis<

a. $.1 I b. 5.! I

c. .0 I

d. 13 I

e. 12 I

%"&' (T&' D)*' %erage



42. % charge of 0 nC is distributed uniforml, along the x axis from x −.0 m to x +.0 m. :hat is the

electric potential relatie to 7ero at infinit, at the point x 5.0 m on the x axis<

a. 5$ I

b. 4! I

c. 3! I

d. 2$ I

e. 100 I

%"&' C (T&' D)*' %erage

4$. Charge of uniform densit, 1 nC#m is distributed along the x axis from x .0 m to x 5.0 m. :hat is

the electric potential relatie to 7ero at infinit, at the origin x 0<

a. 1 I

b. I

c. ! I

d. $4 I

e. 140 I

%"&' (T&' D)*' %erage

4!. % linear charge of nonuniform densit, λ bx/ where b .1 nC#m

/ is distributed along the x axis from x .0 m to x 3.0 m. Determine the electric potential relatie to 7ero at infinit, of the point y 4.0

m on the y axis.

a. 32 I

b. 5 I

c. 10 I

d. 1$ I

e. 15 I


4. % nonuniform linear charge distribution gien b, λ x bx/ where b is a constant/ is distributed along

the x axis from x 0 to x + L. )f b 40 nC#m

and L 0.0 m/ what is the electric potential relatieto a potential of 7ero at infinit, at the point y L on the y axis<

a. 1 I

b. 1$ Ic. 1 I

d. 3 I

e. 14 I


50. % charge of 10 nC is distributed uniforml, along the x axis from x − m to x +3 m. :hich of the

following integrals is correct for the electric potential relatie to 7ero at infinit, at the point x +5 m

on the x axis<

a.

b.

c.



d.

e.

%"&' D (T&' D)*' %erage

51. Charge of uniform linear densit, 3.0 nC#m is distributed along the x axis from x 0 to x 3 m. :hichof the following integrals is correct for the electric potential relatie to 7ero at infinit, at the point x

+4 m on the x axis<

a.

b.

c.

d.

e.

%"&' C (T&' D)*' %erage

5. % charge of 4.0 nC is distributed uniforml, along the x axis from x +4 m to x +2 m. :hich of the

following integrals is correct for the electric potential relatie to 7ero at infinit, at the origin<

a.

b.

c.

d.

e.

%"&' C (T&' D)*' %erage

53. % charge of 0 nC is distributed uniforml, along the y axis from y 0 to y 4 m. :hich of the

following integrals is correct for the electric potential relatie to 7ero at infinit, at the point x +3 mon the x axis<

a.

b.



c.

d.

e.

%"&' % (T&' D)*' %erage

54. Charge of uniform linear densit, 2.0 nC#m is distributed along the x axis from x 0 to x +3 m.

:hich of the following integrals is correct for the electric potential relatie to 7ero at infinit, at the

point y +4 m on the y axis<

a.

b.

c.

d.

e.

%"&' % (T&' D)*' %erage

55. % rod length .0 m is uniforml, charged and has a total charge of 5.0 nC. :hat is the electric

potential relatie to 7ero at infinit, at a point which lies along the axis of the rod and is 3.0 m from

the center of the rod<

a. I

b. 1 I

c. 12 I

d. 5 I

e. 1 I

%"&' C (T&' D)*' %erage

52. % charge of 1! nC is uniforml, distributed along the y axis from y 3 m to y 5 m. :hich of the

following integrals is correct for the electric potential relatie to 7ero at infinit, at the point x + m

on the x axis<

a.

b.

c.



d.

e.

%"&' % (T&' D)*' %erage

5$. Two large parallel conducting plates are !.0 cm apart and carr, eual but opposite charges on their

facing surfaces. The magnitude of the surface charge densit, on either of the facing surfaces is .0

nC#m. Determine the magnitude of the electric potential difference between the plates.

a. 32 I

b. $ I

c. 1! I

d. 45 I

e. 12 I

%"&' C (T&' D)*' %erage

5!. % solid conducting sphere radius 5.0 cm has a charge of 0.5 nC distributed uniforml, on its

surface. )f point % is located at the center of the sphere and point is 15 cm from the center/ what isthe magnitude of the electric potential difference between these two points<

a. 3 I

b. 30 I

c. 15 I

d. 45 I

e. 20 I

%"&' (T&' D)*' %erage

5. Charge of uniform densit, 50 nC#m3 is distributed throughout the inside of a long nonconducting

c,lindrical rod radius 5.0 cm. Determine the magnitude of the potential difference of point % .0

cm from the axis of the rod and point 4.0 cm from the axis.a. .$ I b. .0 I

c. .4 I

d. 1.$ I

e. 3.4 I


20. Charge of uniform densit, 0 nC#m3 is distributed throughout the inside of a long nonconducting

c,lindrical rod radius .0 cm. Determine the magnitude of the potential difference of point % .0

cm from the axis of the rod and point 4.0 cm from the axis.

a. 1. I

b. 1.4 Ic. . Id. .! I

e. 4.0 I

%"&' (T&' D)*' %erage

21. % nonconducting sphere of radius 10 cm is charged uniforml, with a densit, of 100 nC#m3. :hat is the

magnitude of the potential difference between the center and a point 4.0 cm awa,<



a. 1 I

b. 2.! I

c. 3.0 I

d. 4.$ I

e. . I


2. % charge of 40 pC is distributed on an isolated spherical conductor that has a 4.0-cm radius. (oint % is1.0 cm from the center of the conductor and point is 5.0 cm from the center of the conductor.

Determine the electric potential difference V % − V .

a. +1.! I

b. + I

c. +$ I

d. +$. I

e. +.0 I

%"&' % (T&' D)*' %erage

23. Two flat conductors are placed with their inner faces separated b, 2.0 mm. )f the surface charge

densit, on one of the inner faces is 40 pC#m

/ what is the magnitude of the electric potentialdifferences between the two conductors<

a. 32 mI

b. 1! mI

c. 3 mI

d. $ mI

e. 14 mI

%"&' D (T&' D)*' %erage

24. The electric field in a region of space is gien b, E x 3.0 x "#C/ E , E 7 0/ where x is in m. (oints

% and are on the x axis at x% 3.0 m and x 5.0 m. Determine the potential difference V − V %.

a. −4 I

b. +4 I

c. −1! I

d. +30 I

e. −2.0 I

%"&' % (T&' D)*' %erage

25. 8uipotentials are lines along which

a. the electric field is constant in magnitude and direction.

b. the electric charge is constant in magnitude and direction.

c. maximum wor> against electrical forces is reuired to moe a charge at constant speed.

d. a charge ma, be moed at constant speed without wor> against electrical forces.

e. charges moe b, themseles.

%"&' D (T&' 1 D)*' 8as,

22. :hen a charged particle is moed along an electric field line/

a. the electric field does no wor> on the charge.

b. the electrical potential energ, of the charge does not change.

c. the electrical potential energ, of the charge undergoes the maximum change in magnitude.



d. the oltage changes/ but there is no change in electrical potential energ,.

e. the electrical potential energ, undergoes the maximum change/ but there is no change in

oltage.

%"&' C (T&' 1 D)*' 8as,

2$. :hen a positie charge is released and moes along an electric field line/ it moes to a position of

a. lower potential and lower potential energ,.

b. lower potential and higher potential energ,.c. higher potential and lower potential energ,.

d. higher potential and higher potential energ,.

e. greater magnitude of the electric field.

%"&' % (T&' 1 D)*' 8as,

2!. :hen a negatie charge is released and moes along an electric field line/ it moes to a position of

a. lower potential and lower potential energ,. b. lower potential and higher potential energ,.

c. higher potential and lower potential energ,.

d. higher potential and higher potential energ,.

e. decreasing magnitude of the electric field.%"&' C (T&' 1 D)*' 8as,

2. % charge is placed on a spherical conductor of radius r 1. This sphere is then connected to a distant

sphere of radius r not eual to r 1 b, a conducting wire. %fter the charges on the spheres are in

euilibrium/

a. the electric fields at the surfaces of the two spheres are eual.

b. the amount of charge on each sphere is q#.

c. both spheres are at the same potential.d.

the potentials are in the ratio .

e.

the potentials are in the ratio .

%"&' C (T&' 1 D)*' 8as,

$0. The electric potential inside a charged solid spherical conductor in euilibrium

a. is alwa,s 7ero.

b. is constant and eual to its alue at the surface.

c. decreases from its alue at the surface to a alue of 7ero at the center.

d. increases from its alue at the surface to a alue at the center that is a multiple of the

potential at the surface.

e. is eual to the charge passing through the surface per unit time diided b, the resistance.

%"&' (T&' 1 D)*' 8as,

$1. :hich statement is alwa,s correct when applied to a charge distribution located in a finite region of

space<

a. 8lectric potential is alwa,s 7ero at infinit,.

b. 8lectric potential is alwa,s 7ero at the origin.

c. 8lectric potential is alwa,s 7ero at a boundar, surface to a charge distribution.



d. 8lectric potential is alwa,s infinite at a boundar, surface to a charge distribution.

e. The location where electric potential is 7ero ma, be chosen arbitraril,.

%"&' 8 (T&' 1 D)*' 8as,

$. :hich of the following represents the euipotential lines of a dipole<

a.

b.

c.

d.

e.

%"&' 8 (T&' 1 D)*' 8as,

$3. Can the lines in the figure below be euipotential lines<

a. "o/ because there are sharp corners.

b. "o/ because the, are isolated lines.

c. es/ because an, lines within a charge distribution are euipotential lines.d. es/ the, might be boundar, lines of the two surfaces of a conductor.

e. )t is not possible to sa, without further information.

%"&' D (T&' 1 D)*' 8as,

$4. % series of n uncharged concentric shells surround a small central charge q. The charge distributed on

the outside of the nth shell is

a. −nq.



b. −ln nq.

c. +q.

d. +ln nq.

e. +nq.

%"&' C (T&' 1 D)*' 8as,

$5. % series of 3 uncharged concentric shells surround a small central charge q. The charge distributed on

the outside of the third shell isa. −3q.

b. −ln 3q.

c. +q.

d. +ln 3q.

e. +3q.

%"&' C (T&' 1 D)*' 8as,

$2. % series of n uncharged concentric spherical conducting shells surround a small central charge q. The

potential at a point outside the nth shell/ at distance r from the center/ and relatie to V 0 at ∞/ is

a.

.

b.

.

c.

.

d.

.

e.

.

%"&' C (T&' 1 D)*' 8as,

$$. % series of 3 uncharged concentric spherical conducting shells surround a small central charge q. The

potential at a point outside the third shell/ at distance r from the center/ and relatie to V 0 at ∞/ is

a.

.

b.

.

c.

.

d.

.

e.

.

%"&' C (T&' 1 D)*' 8as,



$!. The electric field in the region defined b, the y-z plane and the negatie x axis is gien b, E −ax/

where a is a constant. There is no field for positie alues of x. %s − x increases in magnitude/ relatie

to V 0 at the origin/ the electric potential in the region defined aboe is

a. a decreasing function proportional to −K xK.

b. a decreasing function proportional to −K xK.

c. constant.

d. an increasing function proportional to +K xK.

e. an increasing function proportional to +K x

K.

%"&' 8 (T&' 1 D)*' 8as,

$. The electric field in the region defined b, the y-z plane and the positie x axis is gien b, E ax/

where a is a constant. There is no field for negatie alues of x. %s x increases in magnitude/ relatie

to V 0 at the origin/ the electric potential in the region defined aboe is

a. a decreasing function proportional to −K xK.

b. a decreasing function proportional to −K xK.

c. constant.

d. an increasing function proportional to +K xK.

e. an increasing function proportional to +K xK.

%"&' % (T&' 1 D)*' 8as,

!0. Two charges lie on the x axis/ +3q at the origin/ and −q at x 5.0 m. The point on the x axis where the

electric potential has a 7ero alue when the alue at infinit, is also 7ero is

a. 1.0 m. b. .0 m.

c. .5 m.

d. 3.0 m.

e. 4.0 m.

%"&' D (T&' D)*' %erage

!1. Two charges lie on the x axis/ +q at the origin/ and −3q at x 5.0 m. The point on the x axis where theelectric potential has a 7ero alue when the alue at infinit, is also 7ero is

a. 1.0 m.

b. .0 m.

c. .5 m.

d. 3.0 m.e. 4.0 m.

%"&' (T&' D)*' %erage

!. :hen introduced into a region where an electric field is present/ an electron with initial elocit, will

eentuall, moe

a. along an electric field line/ in the positie direction of the line. b. along an electric field line/ in the negatie direction of the line.

c. to a point of decreased potential.

d. to a point of increased potential.

e. as described in both b and d.

%"&' D (T&' 1 D)*' 8as,



!3. :hen introduced into a region where an electric field is present/ a proton with initial elocit, will

eentuall, moe

a. along an electric field line/ in the positie direction of the line.

b. along an electric field line/ in the negatie direction of the line.

c. to a point of decreased potential.d. to a point of decreased potential.

e. as described in both a and c.

%"&' C (T&' 1 D)*' 8as,

!4. % s,stem consisting of a positiel,-charged particle and an electric field

a. loses potential difference and >inetic energ, when the charged particle moes in the

direction of the field.

b. loses electric potential energ, when the charged particle moes in the direction of the field.

c. loses >inetic energ, when the charged particle moes in the direction of the field.

d. gains electric potential energ, when the charged particle moes in the direction of the field.

e. gains potential difference and electric potential energ, when the charged particle moes in

the direction of the field.

%"&' (T&' 1 D)*' 8as,

!5. % s,stem consisting of a negatiel,-charged particle and an electric field

a. gains potential difference and >inetic energ, when the charged particle moes in the

direction of the field.

b. loses electric potential energ, when the charged particle moes in the direction of the field.

c. gains >inetic energ, when the charged particle moes in the direction of the field.

d. gains electric potential energ, when the charged particle moes in the direction of the field.

e. gains potential difference and electric potential energ, when the charged particle moes in

the direction of the field.

%"&' D (T&' 1 D)*' 8as,

!2. The ohr model pictures a h,drogen atom in its ground state as a proton and an electron separated b,

the distance a0 0.5 × 10−10 m. The electric potential created b, the proton at the position of the

electron is

a. −13.2 I.

b. +13.2 I.

c. −$. I.

d. +$. I.

e. +5.1 × 10 I.

%"&' D (T&' D)*' %erage

!$. The ohr model pictures a h,drogen atom in its ground state as a proton and an electron separated b,

the distance a0

0.5×

10

−10

m. The electric potential created b, the electron at the position of the proton is

a. −13.2 I.

b. +13.2 I.

c. −$. I.

d. +$. I.

e. +5.1 × 10 I.

%"&' C (T&' D)*' %erage



!!. The electric potential at the surface of a charged conductor

a. is alwa,s 7ero.

b. is alwa,s independent of the magnitude of the charge on the surface.

c. ma, be set eual to 7ero b, adding an appropriate constant to the potential at all points of

space.

d. is alwa,s such that the potential is 7ero at all points inside the conductor.

e. is alwa,s such that the potential is alwa,s 7ero within a hollow space inside the conductor.

%"&' C (T&' 1 D)*' 8as,

!. %n electron is released form rest in a region of space where a uniform electric field is present. Hoanna

claims that its >inetic and potential energies both increase as it moes from its initial position to its

final position. &on,a claims that the, both decrease. :hich one/ if either/ is correct<

a. Hoanna/ because the electron moes opposite to the direction of the field. b. &on,a/ because the electron moes opposite to the direction of the field.

c. Hoanna/ because the electron moes in the direction of the field.

d. &on,a/ because the electron moes in the direction of the field.

e. "either/ because the >inetic energ, increases while the electron moes to a point at a

higher potential.

%"&' 8 (T&' D)*' %erage

0. *our electrons moe from point % to point in a uniform electric field as shown below. Lan> the

electrons in diagrams ) through )I b, the changes in potential energ, from most positie to most

negatie when traeling from % to .

a. ) )) ))) )I.

b. )) ))) ; ) ; )I.

c. ))) ; ) )I ; )).

d. )) ; ) )I ; ))).

e. ) ; )) ))) ; )I.

%"&' D (T&' D)*' %erage

1. *our electrons moe from point % to point in a uniform electric field as shown below. Lan> the

electrons in diagrams ) through )I b, the changes in potential from most positie to most negatie

when traeling from % to .

a. ) )) ))) )I.



b. )) ))) ; ) ; )I.

c. ))) ; ) )I ; )).

d. )) ; ) )I ; ))).

e. ) ; )) ))) ; )I.

%"&' C (T&' D)*' %erage

. %n infinite plane of charge with is tilted at a 45° angle to the ertical direction as shown

below. The potential difference/ V B − V A/ in olts/ between points % and / a 4.50 m distance apart/ is

a. −$.02.

b. −.!.

c. −14.11.

d. +$.02.

e. +.!.

%"&' (T&' D)*' %erage

3. %n infinite plane of charge with is tilted at a 45° angle to the ertical direction as shown

below. The potential difference/ V A −

V B/ in olts/ between points % and / a 4.50 m distance apart/ is

a. −$.02.

b. −.!.c. −14.11.

d. +$.02.

e. +.!.

%"&' 8 (T&' D)*' %erage

4. *or the potential / what is the corresponding electric field at the point //<



a.

b.

c.

d.

e. The correct answer is not gien.


PROBLEM

5. Jow much electrical charge is needed to raise an isolated metal sphere of radius 1.0 m to a potential of

1.0 × 102 I<

%"&'

1.1 × 10−4 C

(T&' D)*' %erage

2. )n the ohr model of the h,drogen atom/ the electron circles the proton at a distance of 0.5 × 10−10

m. *ind the potential at the position of the electron.

%"&'

$. Iolts

(T&' D)*' %erage

$. The gap between electrodes in a spar> plug is 0.02 cm. )n order to produce an electric spar> in a

gasoline-air mixture/ the electric field must reach a alue of 3 × 102 I#m. :hat minimum oltage must

be supplied b, the ignition circuit when starting the car<

%"&'1 !00 I

(T&' D)*' %erage

!. To recharge a 1-I batter,/ a batter, charger must moe 3.2 × 105 C of charge from the negatie to the

positie terminal. :hat amount of wor> is done b, the batter, charger< Jow man, >ilowatt hours is

this<

%"&'

4.3 MH/ 1. >:h

(T&' D)*' %erage

Chapter 2"—Capacita!ce a!# $ielectrics

MULTIPLE CHOICE

1. Determine the euialent capacitance of the combination shown when C 1 p*.



a. 4! p* b. 1 p*

c. 4 p*

d. 2.0 p*

e. 5 p*

%"&' D (T&' D)*' %erage

. Determine the euialent capacitance of the combination shown when C 15 m*.

a. 0 m*

b. 12 m*c. 1 m*

d. 4 m*

e. $5 m*

%"&' C (T&' D)*' %erage

3. Determine the euialent capacitance of the combination shown when C 1 n*.

a. 34 n*

b. 1$ n*c. 51 n*

d. 2! n*

e. 1 n*

%"&' (T&' D)*' %erage

4. Determine the euialent capacitance of the combination shown when C 45 µ *.



a. 32 µ *

b. 3 µ *c. 34 µ *

d. 30 µ *

e. 3! µ *

%"&' D (T&' D)*' %erage

5. )f C 10 µ */ what is the euialent capacitance for the combination shown<

a. $.5 µ *

b. 2.5 µ *

c. $.0 µ *

d. 5.! µ *

e. 13 µ *

%"&' D (T&' D)*' %erage

2. :hat is the euialent capacitance of the combination shown<

a. µ *

b. 10 µ *

c.40 µ *d. 5 µ *

e. 2.0 µ *

%"&' (T&' D)*' %erage

$. :hat is the euialent capacitance of the combination shown<



a. 0 µ *

b. 0 µ *

c. µ *

d. 4.2 µ *

e. 2$ µ *

%"&' % (T&' D)*' %erage

!. Determine the euialent capacitance of the combination shown when C 45 µ *.

a. ! µ *

b. 32 µ *

c. 5 µ *

d. 44 µ *

e. 3 µ *

%"&' (T&' D)*' %erage

. Determine the euialent capacitance of the combination shown when C 4 µ *.

a. 0 µ *

b. 32 µ *

c. 12 µ *

d. 45 µ *

e. $ µ *

%"&' C (T&' D)*' %erage



10. Determine the energ, stored in C when C 1 15 µ */ C 10 µ */ C 3 0 µ */ and V 0 1! I.

a. 0.$ mH

b. 0.3 mHc. 0.50 mH

d. 0.1! mH

e. 1.20 mH


11. Determine the energ, stored in C 1 when C 1 10 µ */ C 1 µ */ C 3 15 µ */ and V 0 $0 I.

a. 2.5 mH

b. 5.1 mH

c. 3. mH

d. !.0 mH

e. .! mH

%"&' C (T&' D)*' %erage

1. Determine the energ, stored b, C 4 when C 1 0 µ */ C 10 µ */ C 3 14 µ */ C 4 30 µ */ and V 0 45

I.

a. 3.! mH

b. .$ mH

c. 3. mH

d. . mH



e. !.1 mH

%"&' D (T&' D)*' %erage

13. Determine the charge stored b, C 1 when C 1 0 µ */ C 10 µ */ C 3 30 µ */ and V 0 1! I.

a. 0.3$ mC

b. 0.4 mC

c. 0.3 mC

d. 0.40 mC

e. 0.50 mC

%"&' (T&' D)*' %erage

14. :hat is the total energ, stored b, C 3 when C 1 50 µ */ C 30 µ */ C 3 32 µ */ C 4 1 µ */ and V 0

30 I<

a. 2.3 mH

b. 5 mH

c. 5$ mH

d. 1.2 mH

e. 14 mH


15. Jow much energ, is stored in the 50- µ * capacitor when V a − V b I<



a. 0.$! mH

b. 0.5! mH

c. 0.2! mH

d. 0.4! mH

e. 0. mH

%"&' D (T&' D)*' %erage

12. :hat is the total energ, stored in the group of capacitors shown if the charge on the 30- µ * capacitor is0.0 mC<

a. mH

b. 21 mH

c. 1 mHd. 22 mH

e. 3 mH


1$. :hat is the potential difference across C when C 1 5.0 µ */ C 15 µ */ C 3 30 µ */ and V 0 4 I<

a. 1 I

b. 1 I

c. 12 I

d. 4 I

e. !.0 I

%"&' C (T&' D)*' %erage

1!. :hat total energ, is stored in the group of capacitors shown if the potential difference V ab is eual to

50 I<



a. 4! mH

b. $ mH

c. 3$ mH

d. 1 mH

e. 10 mH

%"&' D (T&' D)*' %erage

1. Determine the energ, stored in the 20- µ * capacitor.

a. .4 mH

b. 3.0 mH

c. 3.2 mH

d. 4.3 mHe. 2.0 mH

%"&' (T&' D)*' %erage

0. Determine the energ, stored in the 40- µ * capacitor.

a. .4 mH

b. 1.2 mH

c. .0 mH

d. . mH

e. 4.0 mH

%"&' C (T&' D)*' %erage



1. )f V % − V 50 I/ how much energ, is stored in the 32- µ * capacitor<

a. 50 mH

b. ! mH

c. 13 mH

d. !. mH

e. 1$ mH

%"&' D (T&' D)*' %erage

. )f V % − V 50 I/ how much energ, is stored in the 54- µ * capacitor<

a. 50 mH

b. 13 mH

c. ! mH

d. !. mH

e. 1$ mH

%"&' (T&' D)*' %erage

3. % 3.0- µ * capacitor charged to 40 I and a 5.0- µ * capacitor charged to 1! I are connected to each

other/ with the positie plate of each connected to the negatie plate of the other. :hat is the final

charge on the 3.0- µ * capacitor<

a. 11 µ C

b. 15 µ C

c. 1 µ C

d. 2 µ C

e. $ µ C


4. % 2.0- µ * capacitor charged to 50 I and a 4.0- µ * capacitor charged to 34 I are connected to each

other/ with the two positie plates connected and the two negatie plates connected. :hat is the total

energ, stored in the 2.0- µ * capacitor at euilibrium<

a. 2.1 mH

b. 5.$ mH

c. 2.2 mH



d. $.0 mH

e. 3.! mH


5. % 5- µ * capacitor charged to 50 I and a capacitor C charged to 0 I are connected to each other/ with

the two positie plates connected and the two negatie plates connected. The final potential difference

across the 5- µ * capacitor is 32 I. :hat is the alue of the capacitance of C <

a. 43 µ *

b. µ *

c. µ *

d. 5! µ *

e. 23 µ *

%"&' C (T&' D)*' Challenging

2. % 4.0-m* capacitor initiall, charged to 50 I and a 2.0-m* capacitor charged to 30 I are connected to

each other with the positie plate of each connected to the negatie plate of the other. :hat is the final

charge on the 2.0-m* capacitor<

a. 0 mC

b. !.0 mC

c. 10 mC

d. 1 mC

e. 30 mC


$. :hen a capacitor has a charge of magnitude !0 µ C on each plate the potential difference across the

plates is 12 I. Jow much energ, is stored in this capacitor when the potential difference across its

plates is 4 I<

a. 1.0 mH

b. 4.4 mH

c. 3. mHd. 1.4 mH

e. 1.$ mH

%"&' (T&' D)*' %erage

!. % 15- µ * capacitor and a 30- µ * capacitor are connected in series/ and charged to a potential difference

of 50 I. :hat is the resulting charge on the 30- µ * capacitor<

a. 0.$0 mC

b. 0.!0 mC

c. 0.50 mC

d. 0.20 mC

e. 0.40 mC

%"&' C (T&' D)*' %erage

. % 15- µ * capacitor and a 5- µ * capacitor are connected in parallel/ and charged to a potential

difference of 20 I. Jow much energ, is then stored in this capacitor combination<

a. 50 mH

b. 1! mH

c. 3 mH



d. $ mH

e. 45 mH

%"&' D (T&' D)*' %erage

30. % 0- µ * capacitor charged to .0 >I and a 40- µ * capacitor charged to 3.0 >I are connected to each

other/ with the positie plate of each connected to the negatie plate of the other. :hat is the final

charge on the 0- µ * capacitor after the two are so connected<

a. 53 mC b. $ mC

c. 40 mC

d. !0 mC

e. 3 mC

%"&' (T&' D)*' %erage

31. % 15- µ * capacitor is charged to 40 I and then connected across an initiall, uncharged 5- µ *

capacitor. :hat is the final potential difference across the 5- µ * capacitor<

a. 1 I

b. 1! I

c. 15 Id. 1 I

e. 4 I

%"&' C (T&' D)*' %erage

3. % 30- µ * capacitor is charged to 40 I and then connected across an initiall, uncharged 0- µ *

capacitor. :hat is the final potential difference across the 30- µ * capacitor<

a. 15 I

b. 4 I

c. 1! I

d. 1 I

e. 40 I

%"&' (T&' D)*' %erage

33. % capacitor of un>nown capacitance C is charged to 100 I and then connected across an initiall,

uncharged 20- µ * capacitor. )f the final potential difference across the 20- µ * capacitor is 40 I/

determine C .

a. 4 µ *

b. 3 µ *

c. 40 µ *

d. 0 µ *

e. 12 µ *

%"&' C (T&' D)*' %erage

34. % 30- µ * capacitor is charged to !0 I and then connected across an initiall, uncharged capacitor of

un>nown capacitance C . )f the final potential difference across the 30- µ * capacitor is 0 I/ determine

C .

a. 20 µ *

b. $5 µ *



c. 45 µ *

d. 0 µ *

e. 4 µ *

%"&' D (T&' D)*' %erage

35. % 30- µ * capacitor is charged to an un>nown potential V 0 and then connected across an initiall,

uncharged 10- µ * capacitor. )f the final potential difference across the 10- µ * capacitor is 0 I/determine V 0.

a. 13 I

b. $ I

c. 0 I

d. I

e. 20 I

%"&' (T&' D)*' %erage

32. % parallel plate capacitor of capacitance C 0 has plates of area A with separation d between them. :hen

it is connected to a batter, of oltage V 0/ it has charge of magnitude Q0 on its plates. )t is then

disconnected from the batter, and the plates are pulled apart to a separation d without discharging

them. %fter the plates are d apart/ the magnitude of the charge on the plates and the potentialdifference between them are

a.

Q0/ V 0 b.

Q0/ V 0c. Q0/ V 0d. Q0/ V 0e. Q0/ V 0

%"&' D (T&' D)*' %erage

3$. % parallel plate capacitor of capacitance C 0 has plates of area A with separation d between them. :hen


disconnected from the batter, and the plates are pulled apart to a separation d without discharging

them. %fter the plates are d apart/ the new capacitance and the potential difference between the platesare

a.

C 0/ V 0 b.

C 0/ V 0c.

C 0/ V 0d. C 0/ V 0e. C 0/ V 0

%"&' C (T&' D)*' %erage



3!. % parallel plate capacitor of capacitance C 0 has plates of area A with separation d between them. :hen

it is connected to a batter, of oltage V 0/ it has charge of magnitude Q0 on its plates. The plates are

pulled apart to a separation d while the capacitor remains connected to the batter,. %fter the plates are

d apart/ the magnitude of the charge on the plates and the potential difference between them are

a.

Q0/ V 0 b.

Q0/ V 0c. Q0/ V 0d. Q0/ V 0e. Q0/ V 0

%"&' (T&' D)*' %erage


it is connected to a batter, of oltage V 0/ it has charge of magnitude Q0 on its plates. The plates are

pulled apart to a separation d while the capacitor remains connected to the batter,. %fter the plates are

d apart/ the capacitance of the capacitor and the magnitude of the charge on the plates are

a.

C 0/ Q0

b.

C 0/ Q0

c. C 0/ Q0

d. C 0/ Q0

e. C 0/ Q0

%"&' % (T&' D)*' %erage


it is connected to a batter, of oltage V 0/ it has charge of magnitude Q0 on its plates. :hile it is

connected to the batter, the space between the plates is filled with a material of dielectric constant 3.

%fter the dielectric is added/ the magnitude of the charge on the plates and the potential difference between them are

a.

Q0/ V 0 b.

Q0/ V 0c. Q0/ V 0d. 3Q0/ V 0e. 3Q0/ 3V 0

%"&' D (T&' D)*' %erage


it is connected to a batter, of oltage V 0/ it has charge of magnitude Q0 on its plates. :hile it is

connected to the batter,/ the space between the plates is filled with a material of dielectric constant 3.

%fter the dielectric is added/ the magnitude of the charge on the plates and the new capacitance are

a.

Q0/ C 0 b.

Q0/ C 0



c. Q0/ C 0d. 3Q0/ C 0e. 3Q0/ 3C 0

%"&' 8 (T&' D)*' %erage

4. The euialent capacitance of the circuit shown below is

a. 0. C.

b. 0.4 C.

c. 1 C.

d. 4 C.

e. 5 C.

%"&' D (T&' 1 D)*' 8as,


a. 0. C.

b. 0.4 C.

c. 1 C.

d. 4 C.

e. 5 C.

%"&' (T&' D)*' %erage


a. 0.50 C.

b. 1.0 C.c. 1.5 C.

d. .0 C.

e. .5 C.

%"&' (T&' 1 D)*' 8as,

45. :hich of the following is not a capacitance<



a.

b.

c.

d.

e.

%"&' 8 (T&' 1 D)*' 8as,

42. % parallel plate capacitor of capacitance C 0 has plates of area % with separation d between them. :hen


disconnected from the batter, and the space between the plates is filled with a material of dielectric

constant 3. %fter the dielectric is added/ the magnitudes of the charge on the plates and the potential

difference between them are

a.Q0/ V 0.

b.

Q0/ V 0.

c. Q0/ V 0.

d. Q0/ 3V 0.

e. 3Q0/ 3V 0.

%"&' (T&' 1 D)*' 8as,

4$. % parallel plate capacitor of capacitance C 0 has plates of area % with separation d between them. :hen


disconnected from the batter, and the space between the plates is filled with a material of dielectricconstant 3. %fter the dielectric is added/ the magnitudes of the capacitance and the potential difference

between the plates are

a.

C 0/ V 0.

b.

C 0/ V 0.

c. C 0/ V 0.

d.

3C 0/ V 0.

e. 3C 0/ 3V 0.

%"&' D (T&' 1 D)*' 8as,

4!. %n initiall, uncharged parallel plate capacitor of capacitance C is charged to potential V b, a batter,.

The batter, is then disconnected. :hich statement is correct<

a. There is no charge on either plate of the capacitor.

b. The capacitor can be discharged b, grounding an, one of its two plates.

c. Charge is distributed eenl, oer both the inner and outer surfaces of the plates.

d. The magnitude of the electric field outside the space between the plates is approximatel,



7ero.

e. The capacitance increases when the distance between the plates increases.

%"&' D (T&' 1 D)*' 8as,

4. % 0.10 p* parallel-plate capacitor is charged to a potential difference of 10.0 I and then disconnected

from the batter,. % cosmic ra, burst creates 1.00 × 102 electrons and 1.00 × 102 positie charges

between the plates. )f the charges do not recombine/ but reach the oppositel, charged plates/ b, how

much is the potential difference between the capacitor plates reduced<a. 1.33 I

b. $.34 I

c. !.2$ I

d. 1/330 I

e. !/2$0 I


50. % 0.12 p* parallel-plate capacitor is charged to 10 I. Then the batter, is disconnected from the

capacitor. :hen 1.00 × 10$ electrons are now placed on the negatie plate of the capacitor/ the oltage

between the plates changes b,

a. −5.0 I. b. −1.1 I.

c. 0 I.

d. +1.1 I.

e. +5.0 I.

%"&' 8 (T&' 3 D)*' Challenging

51. % 0.12 p* parallel-plate capacitor is charged to 10 I. Then the batter, is disconnected from the

capacitor. :hen 1.00 × 10$ positie charges of magnitude KeK are now placed on the positie plate of

the capacitor/ the oltage between the plates changes b,

a. −5.0 I.

b. −1.1 I.c. 0 I.

d. +1.1 I.

e. +5.0 I.


5. % parallel plate capacitor is charged to oltage V and then disconnected from the batter,. Beopold sa,s

that the oltage will decrease if the plates are pulled apart. 6erhardt sa,s that the oltage will remain

the same. :hich one/ if either/ is correct/ and wh,<

a. 6erhardt/ because the maximum oltage is determined b, the batter,.

b. 6erhardt/ because the charge per unit area on the plates does not change.

c. Beopold/ because charge is transferred from one plate to the other when the plates areseparated.

d. Beopold/ because the force each plate exerts on the other decreases when the plates are

pulled apart.

e. "either/ because the oltage increases when the plates are pulled apart.

%"&' 8 (T&' 1 D)*' 8as,



53. %ddition of a metal slab of thic>ness a between the plates of a parallel plate capacitor of plate

separation d is euialent to introducing a dielectric with dielectric constant κ between the plates. The

alue of κ is

a.

.

b. d .

c. d − a.

d.

.

e.

.

%"&' D (T&' D)*' %erage

54. % parallel plate capacitor is connected to a batter, and charged to oltage V . Beah sa,s that the charge

on the plates will decrease if the distance between the plates is increased while the, are still connected

to the batter,. 6ertie sa,s that the charge will remain the same. :hich one/ if either/ is correct/ and

wh,<

a. 6ertie/ because the maximum oltage is determined b, the batter,.

b. 6ertie/ because the capacitance of the capacitor does not change.

c. Beah/ because the capacitance decreases when the plate separation is increased.

d. Beah/ because the capacitance increases when the plate separation is increased.

e. "either/ because the charge increases when the plate separation is increased.

%"&' C (T&' 1 D)*' 8as,

55. :hich of the following statements is incorrect<

a. Capacitance is alwa,s positie.

b. The s,mbol for potential difference between the plates of a capacitor is .

c. :ater is a polar molecule.

d. :hen a dielectric is placed in a capacitor it seres to reduce the electric field.

e. "onpolar molecules cannot be used for dielectric material in a capacitor.

%"&' 8 (T&' 1 D)*' 8as,

52. Two spheres are made of conducting material. &phere N has twice the radius of &phere N1. :hat is the

ratio of the capacitance of &phere N to the capacitance of sphere N1<

a. 1/ since all conducting spheres hae the same capacitance.

b.

c. 4

d. !

e. % single sphere has no capacitance since a second concentric spherical shell is necessar, to

ma>e a spherical capacitor. Thus/ none of the answers aboe is correct.

%"&' (T&' D)*' %erage

5$. :hich of the following materials has the highest dielectric constant<

a. air

b. M,lar

c. paper

d. (,rex glass

e. water



%"&' 8 (T&' 1 D)*' 8as,

5!. )nto the gap between the plates of a parallel plate capacitor of capacitance a slab of metal is

inserted halfwa, between the plates filling one fourth of the gap between the plates. :hat is theresulting new capacitance<

a.

b.

c.

d.

e.

%"&' (T&' D)*' %erage

5. The plates of a parallel plate capacitor of capacitance are hori7ontal. )nto the gap a slab of

dielectric material with is placed/ filling the bottom half of the gap between the plates. :hat is

the resulting new capacitance<

a.

b.

c.

d.

e.


20. %n electric dipole haing dipole moment of magnitude p is placed in a uniform electric field haing

magnitude E . :hat is the magnitude of the greatest change in potential energ, that can happen for this

dipole in this field<a. pE b.

c. 4 pE

d.

e. "o answer gien is correct.

%"&' (T&' 1 D)*' 8as,

PROBLEM

21. )s it feasible to construct an air-filled parallel-plate capacitor that has its two plates separated b, 0.10mm and has a capacitance of 1.0 *< :h, or wh, not<

%"&'

"o. 8ach plate would hae an area of 1.1 × 10$ m

(T&' D)*' %erage



2. Legarding the 8arth and a cloud la,er !00 m aboe the 8arth as the 9plates9 of a capacitor/ calculate

the capacitance if the cloud la,er has an area of 1.0 >m. )f an electric field of .0 × 102 "#C ma>es the

air brea> down and conduct electricit, lightning/ what is the maximum charge the cloud can hold<

%"&'

11.1 n*/ 1$.$ C

(T&' D)*' %erage

23. %n electron is released from rest at the negatie plate of a parallel plate capacitor. )f the distance

between the plates is 5 mm and the potential difference across the plates is 5 I/ with what elocit,

does the electron hit the positie plate< me .1 × 10−31 >g/ qe 1.2 × 10−1 C.

%"&'

1.33 × 102 m#s

(T&' D)*' %erage

24. % 00-olt batter, is connected to a 0.50-microfarad parallel-plate/ air-filled capacitor. "ow the batter,

is disconnected/ with care ta>en not to discharge the plates. &ome (,rex glass is then inserted betweenthe plates/ completel, filling up the space. :hat is the final potential difference between the plates<

The dielectric constant for (,rex is κ 5.2.

%"&'

32 I

(T&' D)*' %erage

Documents

PSE 9e Ch 24 Ch 25 26 Combined Serway