Physics 220 Homework Problems, Fall 2013

Some of these problems are adapted from Serway and Beichner, Physics for Scientistsand Engineers and are used with permission from Harcourt Brace College Publishers.

1-1. A cat slides down a rubber rod and falls from the rodinto a metal pail A resting on a non-conducting shelfwith two other metal pails, B and C, which are incontact, but neither is in contact with A. The shelfbreaks when the cat lands in A, transferring charge toA, and all pails fall separated to the non-conductingfloor. The cat then runs away.(a) At the end of this process the charge on pail A1. is positive.2. is negative.3. is zero.(b) At the end of this process the charge on pail B1. is positive.2. is negative.3. is zero.4. has the same sign as pail A.5. has the same sign as pail C.(c) At the end of this process the charge on pail C1. is positive.2. is negative.3. is zero.4. has the same sign as pail B.5. both (1) and (4) are correct.

1-2. Consider vectors R = (2.10, y = [01] , 1.00) and S = (3.30, 4.00, 0.90).

(a) Calculate the magnitude of R. (b) Calculate the z component of unit vector R.

(c) Calculate the angle between vectors R and S. (d) Calculate the z component of

R× S. [(a) 3.00, 5.00 (b) 0.200, 0.400 (c) 90.0, 110.0 (d) 10.0, 30.0]

1-3. There are identical Q = [02] µC charges located at three positions: (0,−1, 2),

(1, 2, 0), and (−2, 0,−1). Coordinates are listed in units of meters. (a) What is the

magnitude of the force that a charge of −1.00 µC feels at the origin? (b) What is the

angle between this force and the positive x axis? [(a) 5.00× 10−3, 9.00× 10−3 N

(b) 120.0, 130.0]

2-1. A charged particle with a charge of −7.5 pC is placed at the origin where the electricfield (SI units) is E = (3.75 i− 2.90 j). This force is directed toward which quadrant oraxis of the xy plane?1. I2. II3. III4. IV5. +x6. −x7. +y8. −y

2-2. The sketch in the square frame represents two negative pointcharges and one positive point charge, all of the same magnitude.The letters “a” and “b” simply designate two positions within theframe. Note that point “a” is down and to the right from thepositive charge. We label several directions as follows: (1) ↑, (2) ,(3) →, (4) , (5) ↓, (6) , (7) ←, (8) , (9) magnitude is zero,(10) none of the above.

A. What is the approximate direction of the electric field at position “a”?B. What is the approximate direction of the electric field at position “b”?

2-3. In the lab, an object having a net charge of Q = [01] µC is placed in a

uniform electric field of 500 N/C that is directed vertically. What is the mass of this

object if it “floats” in the field? [0.100, 0.300 g]

3-1. Find the area of region bound by the curve y = b− x2 and the x axis, where

b = [01] . [1.00, 7.00]

3-2. A long chain lying along the x axis has linear charge density λ = λa sin2(x) + λb cos2(x),

where λa = [02] C/m and λb = [03] C/m. What is the average

charge density of the chain? Hint: λ = 1T

∫ T0λ(t). [0.50, 1.50 C/m]

3-3. Consider a paraboloid “drinking cup”, as shown. The height ofthe cup is L, and the radius of the cup at the top is a. What isan appropriate differential volume for determining the totalvolume of the cup? The radius r of the cup varies with theheight z according to (r/a)2 = z/L.1. πa2 dz2. 1

2πLa dr3. πa2z dz/L4. 1

2πa2 dL

5. πa2r dz/L

3-4. Consider a cone of height L and base radius a. What is anappropriate differential area for determining the total outersurface area?1. 2πa

√a2 + L2z dz/L2

2. 2πaz dz/L3. 2πa dz/L4. πa2 dz/L2

5. π√a2 + L2 dz

4-1. Two charged particles with charges of ±q = [01] pC are separated by a

distance of a = 0.820 nm. (a) What is the dipole moment of this charge pair? (b) Using

the dipole approximation (d a), what is magnitude of the electric field at a position

along the dipole axis which is a distance of d = 0.915 cm away from the charge pair?

[(a) 5.00× 10−19, 8.00× 10−19 C·m (b) 0.0100, 0.0200 N/C]

4-2. A uniformly charged ring of radius 11.6 cm has a total charge of Q = [02] pC.

What is the magnitude of the electric field on the axis of the ring at a distance of 4.81 cm

from the center of the ring? [1.00, 1.60 N/C]

4-3. A charged hemispherical bowl with radius 13.7 cm and charge

density σ = [03] nC/m2 sits on the xy plane as

shown. Determine the magnitude of (a) the x component,

(b) the y component, and (c) the z component of the vector

electric field at the origin. Hint: Try using spherical coordinates.

[(a) 0, 200 N/C (b) 0, 200 N/C (c) 0, 200 N/C]

5-1. Complete this problem on a separate sheet of paper and submit it with your CID#prominently displayed.(a) Two conducting spheres of the same radius r, carrying equal but opposite charges,are separated by a center-to-center distance of 4r. Sketch the pattern of electric fieldlines in a plane that includes the centers of the two spheres.(b) A negatively charged rod of finite length has a uniform charge per unit length.Sketch the pattern of electric field lines in a plane that includes the rod.

5-2. Consider the pattern of electric field lines in the figure.(a) By counting field lines, rank the left-hand (L) andright-hand (R) charges in order of decreasing magnitude.1. L > R2. R > L3. L = R

(b) Rank the points in the figure according to decreasingelectric field magnitude.1. A = B > C2. C > A = B3. A > C = B4. C > B > A5. A > B > C

(c) The direction of the electric field at point C is1. up2. down3. left4. right5. no direction because magnitude is zero

5-3. An electron is projected from the ground at an angle of 30 above the horizontal at a

speed of v = [01] m/s in a region where an upward electric field has a uniform

magnitude of 400 N/C. Neglecting the effects of gravity, find (a) the time it takes the

electron to return to the ground, (b) the maximum height it reaches along its trajectory,

and (c) its horizontal distance between the launching and landing points.

[(a) 0.100, 0.150 µs (b) 5.0, 15.0 cm (c) 60, 110 cm]

6-1. A uniform electric field E = Exi + Eyj where Ex = [01] N/C and

Ey = [02] N/C, intersects a surface with area of 2.70 m2. What is the

magnitude of the flux through this area if the surface lies (a) in the yz plane? (b) in the

xz plane? (c) in the xy plane? [(a) 0.00, 9.50 N·m2/C (b) 0.00, 9.50 N·m2/C

(c) 0.00, 9.50 N·m2/C]

6-2. Four closed surfaces, S1 through S4, are drawn together with threecharges, −2Q, +Q, and −Q. Rank the four surfaces according to theamount (not magnitude, consider the sign) of electric flux exitingeach one. In answering this problem we are asking about NET flux.[Exiting flux (field lines going out) is canceled by field lines comingin.] That is, summing the net charge enclosed is important.1. S4 > S2 > S1 > S3

2. S3 > S1 > S2 > S4

3. S4 = S2 > S1 > S3

4. S3 > S1 > S2 = S4

5. S2 = S3 > S1 = S4

6-3. A [03] nC point charge is located on the z axis a

distance 0.800 m above the circular end cap of the

paraboloidal cup shown in the figure. If L = 2.00 m and

a = 0.510 m, calculate the magnitude of the total electric flux

due to the point charge (a) through the circular end cap and

(b) through the paraboloidal surface. [(a) 20.0, 40.0 N·m2/C

(b) 20.0, 40.0 N·m2/C]

6-4. A point charge of q = [04] pC is placed at the center of

a regular triangular pyramid with an edge dimension of a = 1 cm.

Determine the total electric flux exiting the pyramid.

[0.500, 0.900 N·m2/C]

7-1. The charge per unit length on a long, straight filament is λ = [01] µC/m.

(a) Determine the electric field at a distance of 2.50 cm from the filament. Here, define +

to mean outward and − to mean inward. (b) Repeat for a distance of 25.0 cm from the

filament. [(a) 400, 600 kN/C (b) 40.0, 60.0 kN/C]

7-2. A square plate of copper with 52.6-cm sides has no net charge and is placed in a uniform

E = [02] kN/C electric field directed perpendicular to the plate. (a) Find the

magnitude of the charge density on each face of the plate. (b) Find the magnitude of the

total charge on each face of the plate. [(a) 10.0, 40.0 nC/m2 (b) 4.00, 9.90 nC]

7-3. A thick conducting shell contains a second conducting shell

as well as three conducting balls with charges of −3 nC, +2

nC, and q = [03] nC, as shown. The conducting

shells have zero net charge. The outer shell has outer radius

5.50 m. (a) Determine the magnitude of the electric field at

point A. (b) Determine the total charge on the inner surface

of the thick shell. (c) Determine the magnitude and

direction of the electric field just outside its outer surface.

Here, + means outward and − means inward.

[(a) 0.00, 3.00 N/C (b) 3.0, 8.0 nC (c) −2.50, 2.50 N/C]

7-4. Complete this problem on a separate sheet of paperand submit it with your CID# prominentlydisplayed.A solid insulating sphere has a uniformly distributedcharge of 1.11 pC, while the thick concentricconducting shell has zero net charge. Assume thata = 10 cm, b =

√2a, c = 2a in the figure.

(a) State Gauss’s law in plain English with noreference to mathematical symbols or acronyms.(b) Graph the total charge enclosed by a concentricGaussian surface of radius r as r varies from 0 to 40cm.(c) Graph the electric field due to this arrangementas a function of radius from r = 0 to 40 cm.

8-1. Another application of Gauss’s law to charged conductors.

In the figure, each of the dots represent a point charge of

q1 = [01] µC. The three conducting shells are

represented by circles and carry a net charge of −1.00 µC,

−2.00 µC, and −3.00 µC on the small, medium, and large

shells, respectively. Find the charge on the outer surface

of the largest shell. [0.0, 20.0 µC]

8-2. An electron is placed half way between two parallel plates (A and B). Plate A is held at0 V and plate B is held at 100 V. The electron will:1. Hit plate A with 0 J of energy.2. Hit plate B with 0 J of energy.3. Hit plate A with 8× 10−18 J of energy.4. Hit plate B with 8× 10−18 J of energy.5. Hit plate A with 1.6× 10−17 J of energy.6. Hit plate B with 1.6× 10−17 J of energy.

8-3. An electron is released from rest in a uniform electric field of magnitude

E = [02] V/m. (a) Through what potential difference will it have passed after

moving 1.24 cm? (b) How fast will the electron be moving after having traveled that

1.24 cm? [(a) 40.0, 90.0 V (b) 4.00× 106, 6.00× 106 m/s]

8-4. A charge of +q is at the origin and a charge of [03] q is at x = 2.000 m. (a) For

what finite positive values of x is the electric potential zero? (b) If q = 1.50 nC, what is

the magnitude of the electric field at this point? [(a) 0.300, 0.700 m (b) 40, 120 N/C]

9-1. A hollow spherical metallic shell of radius of R = 25 cm holds a net surface charge of

Q = [01] pC. (a) Calculate the electric potential at a distance of 2R from the

center of the sphere. (b) Calculate the electric potential at the surface of the sphere.

(c) Calculate the electric potential at the center of the sphere. [(a) −1.00, 1.00 V

(b) −1.00, 1.00 V (c) −1.00, 1.00 V]

9-2. In the presence of a uniform electric field, E = −(6.9 N/C)i + (0.8 N/C)j + Ezk, where

Ez = [02] N/C, assume that the electric potential is −20.00 V at the origin of

the coordinate system, and determine the electric potential at the point 2.7 i− 2.7 k.

[−15.00, 15.00 V]

9-3. A set of equipotential lines are shown in thefigure. Their potential values are shown. Anumber of locations are labeled with dots. Wealso label several directions as follows: (1) ↑,(2) , (3) →, (4) , (5) ↓, (6) , (7) ←,(8) .(a) Which point has the highest electric field?(b) What direction is that highest electric fieldpointing?(c) Which point has the lowest electric field?(d) What direction is that lowest electric fieldpointing?

10-1. A uniformly-charged rod of length L = 2.00 m and charge density λ = 2.65× 10−9 C/m

lies along the x axis with its left end at the origin. Calculate the electric potential at the

point located a distance d = [01] m beyond the end of the rod along the −xaxis. [10.0, 50.0 V]

10-2. A uniformly charged insulating rod of length 60.0 cm is bent into the shape of a

semicircle. If the rod has a total charge of Q = [02] pC. Find the electric

potential at the center of the semicircle. [−2.50, 2.50 V]

10-3. Calculate the electric potential at a point x = 0.489 m

along the axis of the annulus as shown. The annulus

has a uniform charge density of σ = 1.35 µC/m2, an

outer radius of b = 1.13 m and an inner radius of

a = [03] m. [20.0, 60.0 kV]

11-1. An air filled capacitor consists of two parallel plates each with an area of 7.60 cm2,

separated by a distance of [01] mm. If a 20-V potential difference is applied

to these plates, calculate (a) the electric field between the plates, (b) the capacitance,

(c) the charge on each plate, and (d) the surface charge density. [(a) 9.0, 12.0 kV/m

(b) 3.00, 4.00 pF (c) 60.0, 80.0 pC (d) 8.00× 10−8, 9.90× 10−8 C/m2]

11-2. An air filled spherical capacitor is constructed with inner and outer shell radii of 7.0 cm

and [02] cm, respectively. (a) Calculate the capacitance of the device.

(b) What potential difference between the spheres results in a charge of 4.00 µC on the

capacitor? [(a) 10.0, 30.0 pF (b) 100, 400 kV]

11-3. In the following capacitance network,

C1 = [03] µF, C2 = 10.0 µF,

and C3 = 15.0 µF. (a) What is the

equivalent capacitance between points a

and b? (b) If a potential difference of

15 V is applied between points a and b,

what charge is stored on C3?

[(a) 9.0, 12.0 µF (b) 100, 120 µC]

11-4. You have a capacitor connected across a battery. If you wish to increase the total chargedrawn from this battery, which of the following options will work? Choose all of thecorrect answers.1. Add a larger capacitor in series with the first.2. Add a smaller capacitor in series with the first.3. Add a larger capacitor in parallel with the first.4. Add a smaller capacitor in parallel with the first.

12-1. Two capacitors C1 = 25.0 µF and C2 = [01] µF are connected in parallel and

charged with a 100 V power supply. (a) Calculate the total energy stored in the two

capacitors. (b) If the same two capacitors were connected in series, what potential

difference would be required to store [02] mJ of energy? [(a) 0.150, 0.250 J

(b) 50, 150 V]

12-2. A parallel plate air gap capacitor is connected across a 12.0 V potential. At this point it

stores [03] µC of charge. It is then disconnected from the source while still

charged. (a) What is the capacitance of the capacitor? (b) A piece of Teflon is inserted

between the plates. What is the new capacitance? (c) What is the voltage on the

capacitor? (d) What is the charge on the capacitor? [(a) 2.00, 6.00 µF (b) 5.0, 15.0 µF

(c) 5.0, 30.0 V (d) 20.0, 70.0 µC]

12-3. A small rigid object carries positive and negative [04] nC charges. It is

oriented so that the positive charge is at the point (−1.20 mm, 1.10 mm) and the

negative charge is at the point (1.40 mm,−1.30 mm). The object is placed in an electric

field E = (7800 ı− 4900 ) N/C. (a) What is the magnitude of the electric dipole moment

of the object? (b) What is the magnitude of the torque acting on the object? (c) What is

the potential energy of the object in this orientation? (d) If the orientation of the object

can change, what is the difference between its maximum and its minimum potential

energies? [(a) 1.00× 10−11, 3.00× 10−11 C·m (b) 2.00× 10−8, 5.00× 10−8 N·m(c) 1.00× 10−7, 3.00× 10−7 J (d) 2.00× 10−7, 5.00× 10−7 J]

12-4. You have a square parallel plate capacitor (edge length a and separation d). It howeverdoes not fit in the assigned volume of space. You plan to make a second configuration ofequal capacitance. Which of the following options would work?1. half the edge length, and half the separation.2. half the edge length, half the separation, and add a dielectric of constant 2.3. half the edge length, and add a dielectric with κ = 2.5.4. one fourth the edge length and four times the separation.5. one fourth the edge length, twice the separation, and add a dielectric with κ = 8.0.

13-1. A uniform metallic rod, with a cross-sectional area of 1.83 cm2 and a length of 7.08 m,

contains 6.24× 1028 conduction electrons per cubic meter of material, which have a mean

collision time of [01] femtoseconds. (a) Determine the resistivity of the rod.

When the rod experiences a potential difference of 2.52 mV from end to end, determine

(b) the drift velocity of the electrons and (c) the current density in the rod.

[(a) 1.50× 10−8, 3.00× 10−8 Ω·m (b) 1.00× 10−6, 2.00× 10−6 m/s

(c) 10000, 20000± 100 A/m2]

13-2. Suppose that the current through a conductor decreases exponentially with time

according to the expression I(t) = I0e−t/τ , where I0 is the initial current equal to

1.321 mA and τ is a constant equal to [02] s. Consider a piece of the

conductor. (a) How much charge passes through this piece between t = 0 and t = τ?

(b) How much charge passes through this piece between t = 0 and t = 4τ? (c) How much

charge passes through this piece between t = 0 and t =∞? [(a) 1.00, 4.00 mC

(b) 1.00, 4.00 mC (c) 1.00, 4.00 mC]

13-3. A resistor is constructed of a carbon rod that has a uniform cross sectional area of 5.00

mm2. When a potential difference of 15.0 V is applied across the ends of the rod, there is

a current of [03] mA in the rod. What is (a) the resistance of the rod and

(b) the rod’s length? [(a) 2.00× 103, 6.00× 103 Ω (b) 400, 800 m]

14-1. When the voltage across a certain conducting filament is doubled, the current flowingthrough it is observed to increase by a factor greater than two. What type of materialcould the conductor be made of? Hint: Consider the effects of heating.1. copper2. quartz3. lead4. silicon

14-2. The resistance of a platinum wire is to be calibrated for low-temperature measurements.

A platinum wire with a resistance of [01] Ω at 20C is immersed in liquid

nitrogen at 77 K (−196C). If the temperature response of the platinum wire is linear,

what is the expected resistance of the platinum wire in the liquid nitrogen?

(αplatinum = 3.92× 10−3/C) [0.100, 0.400 Ω]

14-3. A toaster is rated at [02] W when connected to a 120-V source. (a) What

current does the toaster carry? (b) What is its resistance? [(a) 4.00, 7.00 A

(b) 10.0, 30.0 Ω]

14-4. An electric car is designed to run off a 12.0-V battery with a total energy storage of

[03] J. (a) If the electric motor draws 8.00 kW, what is the current delivered

to the motor? (b) If the electric motor draws 8.00 kW as the car moves at a steady speed

of 20.0 m/s, how far will the car travel before it is “out of juice”? [(a) 500, 900 A

(b) 30.0, 60.0 km]

15-1. A battery has an emf of 15.00 V. The terminal voltage of the battery is [01] V

when it is delivering 20.00 W of power to an external load resistor R. (a) What is the

value of R? (b) What is the internal resistance of the battery? [(a) 6.00, 9.00 Ω

(b) 1.00, 3.00 Ω]

15-2. Consider the circuit shown. R1 = 5.0 Ω,

R2 = 10.0 Ω, R3 = [02] Ω, and

E = 25.0 V. (a) What is the current in R3?

(b) What is Vb − Va? [(a) 0.100, 0.300 A

(b) 5.00, 6.00 V]

15-3. You have a resistor connected across a battery. If you wish to increase the current drawnfrom the battery, which of the following options will work? Choose all of the correctanswers.1. Add a larger resistor in series with the first.2. Add a smaller resistor in series with the first.3. Add a larger resistor in parallel with the first.4. Add a smaller resistor in parallel with the first.

15-4. A resistor is constructed by shaping a material of resistivity ρ into a hollow cylinder of

length L and with inner and outer radii ra and rb, respectively. The resistivity

ρ = 3.52× 105 Ω·m, L is 4.00 cm, ra = 0.50 cm and rb = [03] cm. (a) The

application of a potential difference between the ends of the cylinder produces a current

parallel to the axis. What is the resistance in this configuration? (b) If the potential

difference is now applied between the inner and outer surfaces, what is the resistance?

[(a) 10.0, 50.0 MΩ (b) 1.00, 2.00 MΩ]

16-1. The current in a circuit is tripled by connecting a [01] -Ω resistor in parallel

with the resistance of the circuit. What is the resistance of the circuit in the absence of

the additional resistor? [400, 900 Ω]

16-2. In the following circuit, R1 = 5.00 Ω, R2 = [02] Ω,

R3 = 25.00 Ω, E1 = 25.00 V, E2 = 15.00 V, and E3 = 5.00 V.

(a) What is I1? (b) What is I2? (c) What is I3? (d) What is the

potential difference across R3? [(a) 0.70, 1.10 A

(b) −0.10, −0.50 A (c) −0.50, −0.70 A (d) 14.0, 17.0 V]

16-3. From the diagram, which of the following are true?1. I1 + I2 + I3 = 02. I1 + I2 = I33. I2 + I3 = I14. I1R+ E + I2R = 05. I1R− I3R = 06. −I2R+ E− I3R = 07. I1R+ I3R = 0

17-1. The circuit shown has been connected for a

long time. R1 = 1.00 Ω,

R2 = [01] Ω, R3 = 4.00 Ω,

R4 = 2.00 Ω, E = 20.0 V, and C = 1.00 µF.

(a) What is the voltage across the

capacitor? (b) If the battery is

disconnected, how long does it take the

capacitor to discharge to one-tenth its initial

voltage? [(a) 5.0, 14.0 V

(b) 4.00× 10−6, 9.90× 10−6 s]

17-2. A [02] -ft extension cord has two 18-Gauge copper wires, each with a diameter

of 1.024 mm. What is the I2R loss in this cord when it carries a current of (a) 1.00 A?

(b) 10.0 A? Note: Because current flows up one wire and down the other, the length of

the current path is twice that of the wire. [(a) 0.050, 0.200 W (b) 5.0, 20.0 W]

17-3. Consider the circuit in the figure.(a) If at some instant the capacitor in this circuit has no charge,what is the current in the resistors?1. 02. E/2R3. E/R4. 2E/R

(b) If at some instant the capacitor in this circuit has charge Q = CE, what is thecurrent in the resistors?1. 02. E/2R3. E/R4. 2E/R

(c) If at some instant the capacitor in this circuit has charge Q = 2CE, what is thecurrent in the resistors?1. 02. E/2R3. E/R4. 2E/R

18-1. The magnetic field of the earth can be reasonably approximated by assuming the

existence of a point dipole at the center of the earth with a dipole moment of

m = 8.00× 1022 A·m2. Using the equation for the magnetic field of a point dipole,

B = (µ0/4π)[3(m · r)r−m]/r3, determine the magnitude and direction of the magnetic

field on the surface of the earth at (a) the equator and (b) the geographic north pole. For

the direction, use + to indicate geographic north and − to indicate geographic south.

Don’t worry about the geomagnetic angle of declination – assume that it is zero. Use

6.37× 106 m as the radius of the earth. [(a) −70.0, 70.0 µT (b) −70.0, 70.0 µT]

18-2. Consider an electron moving near the earth’s equator. It experiences a Lorentz force dueto the earth’s magnetic field. Possible directions for this force include (1) verticallyupward away from the center of the earth, (2) vertically downward towards the center ofthe earth, (3) east, (4) west, (5) north, (6) south, and (7) zero force. What will be thedirection of the force if the electron is moving(a) vertically upward?(b) east?(c) north?

18-3. An electron is projected at a speed of 3.70× 106 m/s in the i + j + k direction into a

uniform magnetic field B = 6.43 i +By j− 8.29 k (Tesla), where By = [01] T.

Calculate (a) the x component, (b) the y component, and (c) the z component of the

resulting vector magnetic force on the electron. [(a) 3.00, 4.00 pN (b) −4.00, −6.00 pN

(c) 1.00, 2.00 pN]

19-1. A thin, horizontal copper rod is 1.29 m long and has a mass of 52.6 g. What is the

minimum current in the rod that can cause it to float in a horizontal magnetic field of

[01] T? [0.100, 0.500 A]

19-2. Assume that in Atlanta, Georgia, the Earth’s magnetic field points northward and

downward at 60 below the horizontal, with a field strength of 52.0 µT. A tube in a neon

sign carries a current of 35.0 mA between two diagonally-opposite corners of a shop

window, which lies in a north-south vertical plane. The current enters the tube at the

bottom south corner and exits at the opposite corner which is [02] m farther

north and 0.85 m higher up. Between these two points, the tube spells out the word

DONUTS. Determine (a) the x component, (b) the y component, and (c) the

z component of the total vector magnetic force on the neon tube. Define coordinate axes

so that the x axis points east, the y axis points north, and the z axis points up.

[(a) −4.00, 4.00 µN (b) −4.00, 4.00 µN (c) −4.00, 4.00 µN]

19-3. A rectangular loop consisting of N = 100 closely

wrapped turns of wire has dimensions a = 0.400 m

and b = 0.300 m and is oriented in a vertical plane so

as to make an angle of 30 with the x axis, as shown.

The loop carries a current I = 1.20 A and

experiences a uniform B = [03] T

magnetic field directed along the +x axis.

(a) Calculate the magnitude of the magnetic moment

of the current-carrying loop. (b) Calculate the

magnitude of the magnetic torque experienced by the

loop. (c) Calculate the magnetic potential energy of

the loop in the field. [(a) 10.0, 20.0 A·m2

(b) 1.00, 4.00 J (c) −1.00, −4.00 J]

20-1. A cosmic-ray proton traveling at [01] c is heading directly toward the center of

the Earth in the plane of Earth’s equator. Assuming that the Earth’s magnetic field has

a uniform magnitude of B = 50.0 µT in the equitorial plane, determine the radius of

motion of the cosmic-ray proton. Neglect relativistic effects if you know about them.

[4.00, 6.00 km]

20-2. At the equator, assume that the earth’s magnetic field is directed northward with a

magnitude of 50 µT and that there is an electric field of 100 N/C directed radially

inward. The Earth’s radius is roughly 6.37× 106 m. A hypothetical charged particle is

orbiting the earth in the equatorial plane and near the earth’s surface at

[02] m/s in an easterly direction under these conditions. What is this

hypothetical particle’s charge to mass ratio (watch the sign)? [−20.0, −40.0 kC/kg]

20-3. A long metallic conductor oriented along the z axis has an

oblong cross section in the xy plane as shown and carries current

in the −z direction (a right-handed coordinate system directs −zinto the page). There is a uniform external magnetic field

present with field lines lying parallel to the xy plane. We label

several directions as follows: (1) ↑, (2) , (3) →, (4) , (5) ↓,(6) , (7) ←, (8) , (9) magnitude is zero, (10) none of the

above. What is the direction of the external magnetic field if the

most negative potential occurs at point A?

21-1. A loop of wire of length L = 10.8 cm is stretched into the shape of a square and carries a

current of I = [01] A. Determine the magnitude of the magnetic field at the

center of the loop due to the current-carrying wire. [10.0, 20.0 µT]

21-2. A conductor consisting of a circular loop of

radius R = [02] m and two straight,

long sections, carries a current of I = 7.00 A. In

the figure, the loop is viewed from the +z

direction. Determine the z component of the

resulting magnetic field at the center of the loop.

[−1.00, −3.00 µT]

21-3. Consider the current carrying loop shown below,

which is formed of radial lines and segments of

circles whose centers are at point P and whose

radii are a = 20.0 cm and b = 50.0 cm. The current

in the loop is I = [03] mA. Assuming

that the loop is viewed from the +z direction,

determine the z component of the resulting

magnetic field at point P . [0.90, 1.30 nT]

21-4. Two long parallel wires, each having mass density

λ = [04] g/m, are supported in the

horizontal plane by strings 6.00 cm long, as shown.

When both wires carry the same current I in opposite

directions, the wires repel each other so that the angle

θ between the supporting strings is 16.0. Determine

the magnitude of the current. [10.0, 30.0 A]

22-1. Two square current-carrying loops and two closed integration paths, one dashed and one

solid, are arranged as shown. If the positive current direction is chosen to be clockwise,

the current in the loop on the left is +10.0 A. Defining ξ =∮

B · ds for a given path, we

find that the ratio ξdashed/ξsolid = [01] . Determine the current (magnitude

and sign) in the right-hand loop. Hint: Draw a top-view diagram of the figure, which

should make the looped paths and current directions more apparent. [−90.0, 90.0 A]

22-2. In the cross-sectional view of a coaxial cable below, the

center conductor is surrounded by a rubber layer,

which is surrounded by an outer conductor, which is

surrounded by another rubber layer. In a particular

application, the current in the inner conductor is

Iinner = [02] mA, directed out of the page,

while the current in the outer conductor is

Iouter = [03] mA, directed into the page.

Determine magnitude and sign of the vertical (up = +)

component of (a) the magnetic field at point a and

(b) the magnetic field at point b. [(a) −40.0, 40.0 µT

(b) −40.0, 40.0 µT]

22-3. A superconducting solenoid with 2000 turns/m is meant to generate a magnetic field of

[04] T. (a) Calculate the current required. (b) Determine the force per unit

length exerted on the windings by this magnetic field. Note that while an individual

current-carrying wire segment experiences no force due to the B-field that it creates, that

wire segment does experience a force due to the collective field produced by all of the

current-carrying coils around the solenoid. [(a) 3.00, 6.00 kA (b) 30.0, 90.0 kN/m]

22-4. Complete this problem on a separate sheet of paperand submit it with your CID# prominently displayed.Two long parallel conducting wires are shown belowin cross section. Both conductors carry equal currentsthat are uniformly distributed over their respectivecross sections. The conductor on the right alwayscarries current into the page. Sketch the y componentof the magnetic field along the x axis from x = −5ato x = +5a under the assumption that the conductoron the left carries current (a) in the same direction asthe conductor on the right and (b) in the oppositedirection as the conductor on the right.

23-1. An ideal solenoid 7.20 cm in diameter and 38.0 cm long has

N = [01] turns and carries 12.0 A of current.

Calculate the magnetic flux through the surface of a disk of

radius 5.00 cm that is positioned perpendicular to and centered

on the axis of the solenoid. [1.00, 5.00 mT·m2]

23-2. Consider the hemispherical closed surface with radius

R = 3.00 cm shown below, which is in a uniform magnetic field

of 0.250 T that makes an angle θ = [02] with the

vertical. (a) Calculate the magnetic flux entering the circular

face of the closed surface. (b) Calculate the magnetic flux

entering through the hemispherical surface.

[(a) −0.700, 0.700 mT·m2 (b) −0.700, 0.700 mT·m2]

23-3. The magnetic field due to a magnetic dipole located at the origin, can be described as a

function of position ~r = rr, via the expression

B =µ0

4π3( ~m · r)r− ~m

r3,

where m is the dipole moment vector. Let a dipole moment of [03] A·m2 be

oriented along the +z direction and imagine a Gaussian sphere of radius 0.750 m

centered on the dipole. (a) Calculate the magnetic flux exiting the upper (+z)

hemisphere. (b) What is the magnetic flux exiting the lower (−z) hemisphere? Hint: Try

using spherical coordinates, and don’t panic. The math is easy. [(a) −50.0, 50.0 µT·m2

(b) −50.0, 50.0 µT·m2]

24-1. When 1.00 g of an unknown material is placed in a north-pointing 50-µT magnetic field,

it is found to exhibit a magnetic moment that points roughly 25 east of north. How

many of the following statements are true of this material? (1) The material is

diamagnetic. (2) The moment will grow with decreasing temperature. (3) The material

exhibits magnetic hysteresis. (4) The material is paramagnetic. (5) Removing the

applied field would eliminate the moment. (6) The moment is permanent. (7) The

moment is induced by the present field. (8) The material is ferromagnetic. (9) The

material has a magnetic domain structure. (10) The material would be weakly repelled

by a strong magnet. (11) The material would be weakly attracted by a strong magnet.

(12) The material could be strongly attracted to a strong magnet. (13) The material

would be attracted to a steel paper clip. (14) The material would not be attracted to a

steel paper clip. (15) χ < 0. (16) µ/µ0 > 1. (17) This is impossible behavior for any

known material.

24-2. A toroid with N = 500 turns, a mean radius of R = 20.0 cm, a coil radius of r = 1.00 cm,

and a powdered steel core with susceptibility χ = [01] , is carrying 2.55 A of

current. Assume that the field is uniform inside the toroid (i.e. R r). (a) Calculate the

magnetic permeability µ of the steel core. (b) Calculate the magnetic field strength µ0H

inside the toroid. (The factor µ0 makes the units the same as those of B.) (c) Calculate

the magnetization µ0M inside the toroid. (d) Calculate the magnetic field B inside the

toroid. [(a) 0.100, 0.300 mT·m/A (b) 1.00, 2.00 mT (c) 0.100, 0.300 T

(d) 0.100, 0.300 T]

24-3. At room temperature (T = 300 K), a paramagnetic gas of density

ρ = 5.00× 1019 molecules/cm3 is subjected to a [02] T magnetic field. The

gas responds with a magnetic moment of 0.01µB per molecule. (a) Determine the

magnetization (magnetic moment per unit volume) of the gas. (b) Determine the

magnetic susceptibility of the gas. (c) Determine the Curie constant of the gas.

[(a) 3.00, 6.00 A/m (b) 1.00× 10−6, 3.00× 10−6 (c) 300, 700 A·K/T·m]

25-1. A uniform magnetic field oscillates in time as B = B0 cos(ωt),

where B0 = [01] T, within a circular region of radius

a = 2.50 cm. A loop of wire containing a single 1.20 V light bulb

surrounds the field-containing region. Determine the oscillation

frequency needed to light the bulb (i.e. to match the emf amplitude

with the light bulb voltage specification). Note: do NOT use the

more appropriate rms quantities if you know about them.

[400, 990 Hz]

25-2. A coil of N2 = 15 turns and radius a = 10.0 cm surrounds a long solenoid of radius

r = 2.00 cm and N1 = 1000 turns/m. If the current in the solenoid varies as

I = I0 cos(ωt), where I0 = [02] A and ω = 120 s−1, determine the maximum

induced emf in the coil. [5.00, 9.00 mV]

25-3. A square coil that consists of 100 turns of wire rotates about a

vertical axis at 1500 rev/s. The horizontal component of the

Earth’s magnetic field at the location of the coil is

[03] µT. Determine the maximum emf induced in the

coil by this field. [30.0, 80.0 mV]

26-1. Use Lenz’s law and Figures (a)–(d) below to answer the following questions concerningthe direction of induced currents.(a) What is the direction of the induced current in resistor R in Fig. (a) when the barmagnet is moved to the left? (1) left (2) right (3) zero current(b) What is the direction of the current induced in the resistor R right after the switch Sin Fig. (b) is closed? (1) left (2) right (3) zero current(c) What is the direction of the induced current in R when the current I in Fig. (c)decreases rapidly to zero? (1) left (2) right (3) zero current(d) A copper bar is moved to the right while its axis is maintained in a directionperpendicular to a magnetic field, as shown in Fig. (d). If the top of the bar becomespositive relative to the bottom, what is the direction of the magnetic field? (1) left(2) right (3) up (4) down (5) into page (6) out of page.

26-2. The square loop shown is made of wires with total

series resistance of 12.6 Ω. It is placed in a uniform

0.117-T magnetic field directed into the plane of the

paper. The loop, which is hinged at each corner, is

pulled as shown until the separation between points A

and B is 3.00 m. If this process takes

t = [01] seconds, what is the average

current generated in the loop (magnitude and sign).

Let “+” indicate clockwise current and “−” indicate

counterclockwise current. [2.00, 3.00 mA]

26-3. A circular loop of wire is moved at constant speed through regions where uniformmagnetic fields of the same magnitude are directed into or out of the paper, as indicated.The instantaneous location of the loop, as it moves to the right, is indicated at sevenpositions.(a) At how many of the seven positions will there be no induced emf in the loop?(b) At how many of the seven positions will there be a CW induced emf in the loop?(c) At how many of the seven positions will there be a CCW induced emf in the loop?(d) At which position will the magnitude of the induced emf be maximum?

26-4. An electric motor consists of a rectangular coil (2.50 cm × 4.00 cm) with 80 turns of wire

that draws I = [02] A of current as it rotates at 3600 rev/min in a uniform

B = 0.800 T magnetic field. (a) Determine the maximum torque delivered by the motor.

(b) Determine the peak power produced by the motor. [(a) 0.100, 0.300 J

(b) 40.0, 99.0 W]

27-1. A helicopter has blades with a length of 3.00 m extending outward from a central hub

and rotating at f = [01] rev/s. If the vertical component of the Earth’s

magnetic field is 50.0 µT, what is the emf induced between the blade tip and the center

hub? [1.00, 3.00 mV]

27-2. A conducting axle with mass m = [02] kg and length L = 1.50 m long rolls at

constant velocity along a pair of conducting rails that are inclined 30 from the

horizontal. A resistive load R = 100 Ω connects the rails, which are immersed in a

uniform 0.800 T magnetic field that points downward. (a) Determine the magnitude of

the magnetic force on the axle. (b) Determine the speed of the rolling axle. Hints: Draw

a free-body diagram. Separate forces into components, parallel and perpendicular to the

rail. Take the inclination angle into account when computing the induced emf.

[(a) 50.0, 99.0 N (b) 4.00, 8.00 km/s]

27-3. A closed rectangular wire loop has dimensions

w = 0.80 m, ` = 1.50 m, mass m = [03] g,

and resistance R = 0.750 Ω. The rectangle is allowed to

fall through a region of uniform magnetic field, directed

out of the page as shown, and accelerates downward as

it approaches a terminal speed of 2.00 m/s with its top

not yet in the region of the field. Calculate the

magnitude of the magnetic field. [0.400, 0.700 T]

28-1. A 10.0-mH inductor carries a current of I = Imax sinωt with Imax = 5.00 A and

ω/2π = 60.0 Hz. What is the magnitude of the back emf at t = [01] s?

[0.0, +20.0 V]

28-2. For the RL circuit shown, let L = 3.00 H, R = 8.00 Ω, and

E = [02] V. The switch is closed at t = 0.

(a) Calculate the ratio of the potential difference across the

resistor to that across the inductor when I = 2.00 A.

(b) Calculate the voltage across the inductor [03] s

after the switch is closed. [(a) 0.60, 1.20 (b) 0.100, 0.800 V]

28-3. Two coils, held in fixed positions, have a mutual inductance of 130 µH. What is the peak

voltage in one when a sinusoidal current given by I(t) = Imax sin(ωt) flows in the other?

Imax = 12.0 A and ω = [04] s−1. [1.00, 1.50 V]

28-4. A [05] -V battery, a 5.00-Ω resistor, and a 12.0-H inductor are connected in

series. After the current in the circuit has reached its maximum value, calculate (a) the

power being supplied by the battery, (b) the power being delivered to the resistor, (c) the

power being delivered to the inductor, and (d) the energy stored in the magnetic field of

the inductor. [(a) 20.0, 99.0 W (b) 20.0, 99.0 W (c) 0.0, 99.0 W (d) 20.0, 99.0 J]

29-1. The switch in the circuit shown is connected to

point a for a long time. R = 14.0 Ω,

L = 0.110 H, C = [01] µF, and

E = 12 V. After the switch is thrown to point b,

what are (a) the frequency of oscillation of the

LC circuit, (b) the maximum charge that

appears on the capacitor, (c) the maximum

current in the inductor, and (d) the total

energy the circuit possesses at t = 3.00 s?

[(a) 400, 500 Hz (b) 10.0, 20.0 µC

(c) 30.0, 50.0 mA

(d) 7.00× 10−5, 9.90× 10−5 J]

29-2. In the figure, let R = 7.60 Ω, L = [02] mH, and

C = 1.80 µF. (a) Calculate the frequency of the damped

oscillation of the circuit. (b) What is the critical resistance?

[(a) 2.00× 103, 3.00× 103 Hz (b) 60.0, 90.0 Ω]

29-3. The switch in the figure is thrown closed at t = 0.

R = 75 Ω, E = [03] V, C = 1.80 µF, and

L = 2.20 mH. Before the switch is closed, the capacitor is

uncharged and all currents are zero. The instant after the

switch is closed, determine the currents in (a) L, (b) C,

and (c) R. Also determine the potential differences across

(d) L, (e) C, and (f) R. A long time after the switch is

closed, determine the potential differences across (g) L,

(h) C, and (i) R. [(a) 0.000, 0.500 A (b) 0.000, 0.500 A

(c) 0.000, 0.500 A (d) 0.0, 40.0 V (e) 0.0, 40.0 V

(f) 0.0, 40.0 V (g) 0.0, 40.0 V (h) 0.0, 40.0 V

(i) 0.0, 40.0 V]

30-1. An inductor is connected to a 20.0-Hz power supply that produces a 50.0-V peak voltage.

What inductance is needed to keep the instantaneous current in the circuit below

[01] mA? [4.00, 7.00 H]

30-2. What maximum current flows through a [02] -µF capacitor when it is

connected across (a) a North American outlet having Vrms = 120 V and f = 60.0 Hz?

(b) a European outlet having Vrms = 240 V and f = 50.0 Hz? [(a) 0.100, 0.400 A

(b) 0.100, 0.400 A]

30-3. (a) Draw to scale a phasor diagram showing Z, XL, XC , and φ for an AC series circuit

with R = [03] Ω, C = 11.0 µF, L = 0.200 H, and f = (500/π) Hz. Submit

this part of the problem to the 220 homework bins on a single sheet of paper before class.

Include your CID!!! (b) What is Z? (c) What is the phase angle φ? [(b) 200, 500 Ω

(c) 10.0, 30.0]

31-1. A series RLC circuit is used in a radio to tune in to an FM station broadcasting at

99.7 MHz. The resistance in the circuit is 12.0 Ω, and the inductance is

[01] µH. What capacitance should be used? [1.00, 3.00 pF]

31-2. In a certain series RLC circuit, Irms = 9.00 A, Vrms = 180 V, and the current leads the

voltage by [02] . (a) What is the resistance R of the circuit? (b) What is the

reactance of the circuit (XL −XC)? [(a) 5.0, 20.0 Ω (b) 5.0, 20.0 Ω]

31-3. In a series RLC circuit, R = [03] Ω, XC = 150 Ω, XL = 100 Ω,

E = 100 V (rms), and f = [04] Hz. (a) Find L. (b) Find C. (c) Find the rms

current flowing in the circuit. (d) Find the phase shift φ. (e) Find the power dissipated.

(f) Find the ratio of VCmax/VRmax . [(a) 0.100, 0.400 H (b) 10.0, 25.0 µF

(c) 0.300, 0.700 A (d) −90.0, +90.0 (e) 30.0, 70.0 W (f) 0.50, 2.00]

32-1. A step down transformer is used for recharging the batteries of a portable device such as

a tape player. The turns ratio inside the transformer is 13:1, and it is used with 120 V

(rms) household service. If a particular ideal transformer draws [01] A (rms)

from the house outlet, (a) what (rms) voltage is supplied to the tape player from the

transformer? (b) What (rms) current is supplied to the tape player from the transformer?

(c) How much power is delivered? [(a) 5.00, 9.50 V (b) 3.00, 6.00 A (c) 30.0, 50.0 W]

32-2. Over a distance of 110 km, power of 130 MW is to be transmitted at [02] kV

(rms) with only 1.50% loss. Copper wire of what diameter should be used for each of the

two conductors of the transmission line? Assume that the current density in the

conductors is uniform and remember that the resistivity of copper is 1.70× 10−8 Ω·m.

Note: Because current flows up one wire and down the other, the length of the current

path is twice that of the wire. [0.100, 0.300 m]

32-3. A transformer is shown in the figure. The

load resistor RL = 50.0 Ω. The turns ratio

N1:N2 is 5:2, and the source voltage is 80.0 V

(rms). If a voltmeter across the load measures

[03] V (rms), what is the source

resistance Rs? [20.0, 90.0 Ω]

33-1. An air-filled circular parallel plate capacitor with radius a = 5.00 cm and plate

separation d = 2.00 mm, is driven by a 60 Hz alternating voltage with amplitude

V = [01] V. Naturally, the magnitude of the current is greatest at the instant

when the voltage is zero. At such an instant, determine the magnitude of the (a) rate of

change of electric flux in the capacitor, (b) displacement current in the capacitor, and

(c) magnetic field near the edge of the capacitor. [(a) 100, 300 kV·m/s (b) 1.00, 3.00 µA

(c) 5.00, 9.99 pT]

33-2. Which of the following laws or principles are required to solve the problems describedbelow. In each case, choose only one answer. If more than one response seemsappropriate, choose the one most fundamental to the problem at hand. Possibleresponses are: (1) Gauss’s law of electrostatics, (2) Gauss’s law of magnetism,(3) Faraday’s law, (4) Ampere-Maxwell law, (5) Lorentz force law.(a) Determine the magnetic field near a current carrying wire.(b) Determine the trajectory of a proton in a uniform magnetic field.(c) Determine the electric field inside a charged capacitor.(d) Determine the magnetic field inside a charging capacitor.(e) Determine the power delivered by a wind-turbine generator.(f) Determine the electric field near the surface of a conductor.(g) Determine the voltage difference between the ends of a metal bar moving in amagnetic field.(h) Determine the total magnetic flux through a closed surface.(i) Determine the voltage in the secondary winding of a transformer.(j) The magnetic field produced by a moving charged particle.

33-3. Determine the validity of each of the following statements. Possible responses are(1) True or (2) False.(a) Ampere’s law is physically equivalent to the Lorentz force law.(b) Gauss’s law of electrostatics is physically equivalent to Gauss’s law of magnetism.(c) Coulomb’s law is physically equivalent to Gauss’s law of electrostatics.(d) The Biot-Savart law is physically equivalent to Faraday’s law.(e) Lenz’s law is a corollary of Faraday’s law.(f) Gauss’s law of electrostatics relates electric charge to electric flux.(g) Gauss’s law of magnetism relates magnetic charge to magnetic flux.(h) The Ampere-Maxwell law relates magnetic circulation to changing electric flux.(i) The Ampere-Maxwell law relates magnetic circulation to electric current.(j) Faraday’s law relates electric charge to changing magnetic flux.

33-4. Complete this problem on a separate sheet of paper and submit it with your CID#prominently displayed.Name and state each of Maxwell’s equations and the Lorentz force law in plain Englishwith no reference to symbols or acronyms.

34-1. A transverse wave on a string is described by the wave function y = y0 sin(kx+ ωt),

where y0 = [01] m, k = [02] m−1, and ω = [03] s−1. At

time t = 0.200 s and string position x = 1.6 m, determine the following quantities:

(a) Wavelength.

(b) Wavenumber.

(c) Wave frequency (cyclic).

(d) Wave period. (e) Wave velocity (magnitude and sign).

(f) Transverse string position (magnitude and sign).

(g) Peak transverse string position (magnitude).

(h) Average transverse string position (magnitude).

(i) Transverse string velocity (magnitude and sign).

(j) Transverse string acceleration (magnitude and sign).

[ (a) 10.0, 25.0 m (b) 0.200, 0.600 m−1 (c) 1.00, 3.00 Hz (d) 0.400, 0.700 s

(e) −60.0, +60.0 m/s (f) −0.150, 0.150 m (g) 0.000, 0.150 m (h) −0.150, 0.150 m

(i) −3.00, +3.00 m/s (j) −40.0, +40.0 m/s2 ]

34-2. The speed of an electromagnetic wave traveling in a transparent nonmagnetic substance

is 1/√µ0κε0, where κ is the dielectric constant of the substance, which depends on

frequency. Determine the speed of light in a liquid with a dielectric constant of

κ = [04] at optical frequencies. FYI, water has a dielectric constant of 1.78 in

this range. [2.00× 108, 3.00× 108 m/s]

34-3. A standing-wave interference pattern is set up by radio waves between two metal sheets

d = [05] m apart. This is the shortest distance between the plates that will

produce a standing-wave pattern. What is the fundamental frequency of the radio waves?

[50.0, 95.0 MHz]

34-4. Match the following object sizes to the wavelength of the appropriate electromagneticradiation. Possible responses are (1) gamma rays, (2) x-rays, (3) ultraviolet rays,(4) visible light, (5) infrared, (6) microwaves, (7) FM radio waves, (8) AM radio wave,(9) long-wavelength radiation.(a) An atom.(b) Your finger.(c) Your height.(d) The thickness of a human hair.(e) A bacterium(f) A virus.(g) An atomic nucleus.(h) Your campus.(i) Your world (which may also be your campus).

35-1. Neldon the Nerd went to see Star Wars and was fascinated by the red light pulses from

the laser blasters. He decides to make such a weapon. He chooses a pulsed laser with a

wavelength of 580 nm so that the light will be red.

(a) The pulses in the movie appeared to be L = [01] m long and lasted

roughly 0.2 seconds. But Neldon is annoyed to discover that a light pulse this long must

have a temporal duration of only .

(b) Neldon can’t make such a pulse, but does manage to build a gun with a

T = [02] µs pulse. At t = 0, when the pulse begins, E is exactly zero at the

muzzle of the gun. During the length of the pulse, E will be zero again more

times.

(c) Neldon decides to blast the white clock on the wall across the room since its white

reflective surface resembles that of a storm trooper uniform. A short time after the small

spot of light strikes near the center of the clock face, the electric field points toward

M = [03] minutes after 12 o’clock. At this same instant, the magnetic field

points toward minutes after 12 o’clock.

[(a) 1.00, 4.00 ns (b) 1.00× 109, 3.00× 109 (c) 0.0, 59.9 min]

35-2. Neldon then adjusts the pulse length of his laser blaster to 2.00 µs and the beam

diameter to D = [04] mm. Though he finds that his laser pulse has an

impressive total energy of E = [05] kJ, he is again annoyed when the clock

doesn’t shatter. (a) So he computes the momentum delivered by the pulse assuming

complete reflection, and finds it to be a mere . He then calculates (b) the average

beam intensity, (c) the peak beam intensity, (d) the peak E-field magnitude, and (e) the

peak B-field magnitude. [(a) 2.00× 10−5, 4.00× 10−5 kg·m/s (b) 5.00× 1014, 9.00× 1014

W/m2 (c) 1.00× 1015, 2.00× 1015 W/m2 (d) 6.00× 108, 9.00× 108 N/C (e) 2.00, 3.00 T]

35-3. Neldon finally gives up on laser blasters and figures that a light saber would be much

more practical. Using a tunable continuous-output laser this time and a pair of parallel

adjustable mirrors, he decides to create a first-harmonic standing wave. After settling on

blue as the ideal color for a light saber, he picks a wavelength of λ = [06] nm.

(a) Much to Neldon’s surprise, the required mirror separation calculates to be .

(b) He decides that color isn’t all that important after all and sets the mirror separation

to a more reasonable [07] m. Now he obtains a wavelength of , which

doesn’t reflect off the mirror well, but does interfere with his FM radio. While he still

doesn’t know how to get the color right, he figures that this must be the origin of the

cool sound that light-sabers make. [(a) 200, 300 nm (b) 1.00, 2.00 m]

36-1. An AM radio station broadcasts isotropically (equally in all directions) with an average

power of 4.00 kW. An optimally-oriented λ/2 dipole antenna 65.0 cm long is located

d = [01] km from the transmitter. (a) Compute the maximum E-field at the

receiving antenna. (b) Compute the maximum B-field at the receiving antenna.

Compare this to the magnetic field of the earth, which is roughly 50 µT. (c) Compute the

maximum emf induced by this signal between the two ends of receiving antenna.

[(a) 0.300, 0.500 N/C (b) 1.00, 2.00 nT (c) 0.200, 0.400 V]