General Physics II, Lec 4, By/ T.A. Eleyan 1 Lecture 4 Discussion

General Physics II, Lec 4, By/ T.A. Eleyan

1

Lecture 4

Discussion


2

[1 ]In figure, two equal positive charges q=2x10-6C interact with a third charge Q=4x10-6C. Find the magnitude and direction of the resultant force on Q.

0

46.0

0sinsin

46.023.02)5

4(29.0cos2

29.0)5.0(

)102)(104(109

2

669

21

1 2

NF

FFF

NFF

N

r

qQKFF

T

y

x

eQqQq


3

[2 ]A charge Q is fixed at each of two opposite corners of a square as shown in figure. A charge q is placed at each of the other two corners. If the resultant electrical force on Q is Zero, how are Q and q related.

12 13

2 2

13 14

2 2

0 cos 0

1.

2 2

....................................(1)2 20 sin 0

1.

2 2

....................................(1)2 2

2 2

x

y

F F F

kQq kQQ

a a

Qq

F F F

kQQ kQq

a a

Qq

then

Q q


4

[3 ]Two fixed charges, 1µC and -3µC are separated by 10cm as shown in figure (a) where may a third charge be located so that no force acts on it? (b) is the equilibrium stable or

unstable for the third charge?

31 32

3 1 3 22 2

31 32

6 6

22

22 2 2

1 10 3 10

10

3 10 3 20 100

e e

F F

q q q qK K

r r

d d

d d d d d


5

2 2

2

2 20 100 0 10 50 0

1. 10, 50

10 100 4(1)( 50)4

2 2

10 10 310 300 2

2 2

5 5 3 13.66

5 5 3 13.66

)the equilibrium unstable

d d d d

a b c

b b acd

a

d

d

d

b s


6

[4 ]Find the electric field at point p in figure due to the charges shown.

Solution: 1 2

4

3

4

2 2

36 10 /

28 10 /

( ) ( )

46.1 /

141

x

y

p x y

E E E

N C

E E

N C

E E E

N C


7

[5 ]A charged cord ball of mass 1g is suspended on a light string in the presence of a uniform electric field as in figure. When E=(3i+5j) *105N/C, the ball is in equilibrium at Θ=37o. Find (a) the charge on the ball and (b) the tension in the string.

Substitute T from equation (1) into equation (2)

5

5

3 10 /

5 10 /

sin 37 0....(1)

cos37 0....(2)

x

y

x x

y y

E N C

E N C

F qE T

F qE T

Substitute T from equation (1) into equation (2)

Substitute by q into equation (1) to find T=5.44*10-3N


8

[6 ]A 1.3µC charge is located on the x-axis at x=-0.5m, 3.2µC charge is located on the x-axis at x=1.5m, and 2.5µC charge is located at the origin. Find the net force on the 2.5µC charge

NFFF

r

qqKF

r

qqKF

t

e

e

3332321

32

669

223

3223

32

669

221

2121

10149103210117

10325.1

105.2102.3109

101775.0

105.2103.1109


9

[7 ]Two free point charges +q and +4q are a distance 1cm apart. A third charge is so placed that the entire system is in equilibrium. Find the location, magnitude and sign of the third charge. Is the equilibrium

stable?

md

md

d

dd

ddd

dd

d

qK

d

qK

EE

ee

3/1

16

13442

0123

012_4

14

1

4

2

22

22

22

21


10

[8] Two protons in a molecule are separated by a distance of 3.8*10-10m. Find the electrostatic force exerted by one proton on the other.

[9] The electric force on a point charge of 4.0mC at some point is 6.9*10-

4N in the positive x direction. What is the value of the electric field at that point?

9

21

9

210

999

221 106.1

104.14

106.14.14

108.3

106.1106.1109

r

qqKF e

CNq

FE 2

6

4

10725.1100.4

109.6


11

[10 ]Two point charges are a distance d apart . Find E points to the left P. Assume q1=+1.0*10-6C, q2=+3.0*10-6C, and d=10cm

2

6

2

69

21

2

69

22

22

2

69

21

11

10

100.3100.1109

10

100.3109

100.1109

xxEEE

xr

qKE

xr

qKE

PPT

eP

eP


12

]11[ Calculate E (direction and magnitude) at point P in Figure.

22

31

2

0

r

qkEE

EEE

ey

x

it fromaway triangle theof middle From

4.

4

1

2

2.

4

1

2

2

20

20

20

2

a

qE

a

q

a

q

a

qkEE eyT


13

[12 ]A uniform electric field exists in a region between two oppositely charged plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate, 2.0cm away, in a time 1.5*10-8s. (a) What is the speed of the electron as it strikes the

second plate? (b) What is the magnitude of the electric field.

20

0

6

3

:

1/ 2

2.7 10 /

/ / 1 10 /

Horizental

first find the acceleration from the relation

x v t at

then find the velocity

v v at

v m s

then find the electric field E F q ma q N C


14

[13 ]Three charges are placed on corners of an equilateral triangle as shown in Figure 1. An electron is placed at the center of the

triangle. What is the magnitude of the net force on the electron?

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iselectrontheonforcenettheand

Nr

cekF

isforcesthreetheofeachofmagnitudetheThus

mrr

yxnet922

92

106.82

103.41

,

577.05.0

30cos


15

[14 ]A uniform electric field exists in the region between two oppositely charged plane parallel plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate 2x10-8 s later. If the magnitude of the electric field

is 4x103 N/C, what is the separation between the plates ?

matd

bygivenisdistncetherestfromstartselectrontheSince

smm

eE

m

Fa

ee

14.0)102)(107(2

1

2

1

,

/107

28142

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General Physics II, Lec 4, By/ T.A. Eleyan 1 Lecture 4 Discussion