1.

Two small spheres, each with mass m = 5.0 g and charge q, are suspended from a point

by threads of length L = 0.30 m. What is the charge on each sphere if the threads make

an angle = 20º with the vertical?

B) 2.9 10–7

C

2.

y

x

2Q Q

0 a

A charge 2Q is located at the origin while a second charge Q is located at x = a. Where

should a third charge be placed so that the net force on the charge is zero?

C) x > a

3.

Three charges Q1, Q2, and Q3, each equal to 6.4 10

–19 C, are in a straight line. The

distance between neighboring charges is 60 nm. The magnitude of the electric field at

P, which is 80 nm from Q2 on a line at right angles to the line

between Q1 and Q3, is

D) 1.9 1010

N/C

4.

Three charges, each of Q = 3.2 10

–19 C, are arranged at three of the corners of a 20-nm

square as shown. The magnitude of the electric field at D, the fourth corner of the

square, is approximately

A) 1.4 107 N/C

Section: 21–4 Topic: The Electric Field Type: Conceptual

5. An electric field with a magnitude of 6.0 104 N/C is directed parallel to the positive y

axis. A particle with a charge q = 4.8 10–19

C is moving along the x axis with a speed

v = 3.0 106 m/s. The force on the charge is approximately

B) 2.9 10–14

N in the y direction.

6.

A bob of mass m (m = 0.500 g), and charge magnitude Q (Q = 50.0 C) is held by a

massless string in a uniform electric field E. If the bob makes an angle of 10.0 degrees

with the vertical, then calculate the magnitude of the electric field E and the sign of the

bob charge Q.

A) 1.73 101 N/C and Q is positive.

m

q

E

T

7. The tension T in the string is ____ the weight mg.

A) less than

Section: 21–4 Topic: The Electric Field Type: Numerical

8. If m = 1 g, q = 1 C and E = 5000 N/C, the tension T in the string is

C) 4.81 10-3

N

9.

A small positive charge is located at A. The vector that gives the direction of the

electric field at point P is

B) 2

10.

The point P is on the axis of a ring of charge, and all vectors shown lie in the yz plane.

The negatively charged ring lies in the xz plane. The vector that correctly represents the

direction of the electric field at this point is

A) 1

11.

The figure shows the field lines for two charges. What is the ratio of the top charge to

the bottom charge?

D) 2:1

12. In a uniform electric field a proton has

C) an approximately constant acceleration the direction of the field.

Use the picture for the next two problems.

qv

E1

2

3

4

w

A negatively charged particle moving with speed v enters a region of uniform electric

field E.

13. If nonelectric forces are negligible, a positively charged particle released from rest

in a nonuniform electric field

C) accelerates in the direction of the field.

14. Using the direction compass on the right, the direction of the force on the charge is

C) 3

15. If the charge q = 1 nC, mass m = 1 10-14

kg, speed v = 105 m/s, the electric field

strength E = 2 105 V/m, and width, w, of the electric field is 0.2 m, what is the speed

of the particle when it emerges from the other side?

C) 1.08 105 m/s

16. An electric dipole p of magnitude 25 p C · m makes an angle of 65º with a uniform

electric field E of magnitude 3.0 10–6

N/C. What is the magnitude of the torque on

the dipole?

D) 6.8 10–16

N · m

17. A disk of radius 10 cm carries a uniform surface charge density of 6.0 µC/m2.

The electric field on the axis of the disk at a distance of 10 cm is approximately

C) 99 kN/C

18. An infinite plane lies in the yzplane and it has a uniform surface charge density.

The electric field at a distance x from the plane

C) is constant and does not depend on x.

19. A uniform circular ring has charge Q = 7.36 C, and radius r = 3.33 cm. Calculate the magnitude

of the electric field at a distance of 4.20 cm along the axis of the ring.

E) 1.81 107 N/C

20.

A cubical surface with no charge enclosed and with sides 2.0 m long is oriented with right and

left faces perpendicular to a uniform electric field E of (1.6 105 N/C) i . The net electric flux E

through this surface is approximately

A) zero

21. Consider a uniform electric field E = (5.0 kN/C) i . What is the flux of this field through

a square of side 20 cm in a plane parallel to the yz plane?

B) 0.20 kN · m2/C

22.

The figure shows a surface enclosing the charges 2q and –q. The net flux through the

surface surrounding the two charges is

23.

A rod of infinite length has a charge per unit length of (= q/l). Gauss's law makes it easy to

determine that the electric field strength at a perpendicular distance r from the rod is, in terms

of k = (40)–1,

D) 2k/r

24. A sphere of radius 8.0 cm carries a uniform volume charge density = 500 nC/m3. What is the

electric field at r = 8.1 cm?

B) 1.5 kN/C

25. An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density

= 200 nC/m3. What is the electric field at r = 8.0 cm?

A) 0.23 kN/C

26. A spherical shell of radius 9.0 cm carries a uniform surface charge density

= 9.0 nC/m2. The electric field at r = 4.0 cm is approximately

E) zero

Section: 22–3 Topic: Using Symmetry to Calculate E with Gauss’s Law

Type: Numerical

27. A spherical shell of radius 9.0 cm carries a uniform surface charge density

= 9.0 nC/m2. The electric field at r = 8.9 cm is approximately

D) zero 28.

An infinite plane of surface charge density = +8.00 nC/m2 lies in the yz plane at the origin,

and a second infinite plane of surface charge density = –8.00 nC/m2 lies in a plane parallel to

the yz plane at x = 4.00 m. The electric field at x = 3.50 m is approximately

C) 904 N/C

29.

An infinite plane of surface charge density = +8.00 nC/m2 lies in the yz plane at the origin,

and a second infinite plane of surface charge density = –8.00 nC/m2 lies in a plane parallel to

the yz plane at x = 4.00 m. The electric field at x = 5.00 m is approximately

E) zero

Use the following scenario for the next three questions.

Qra

rb1

rb2

A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of

inner radius rb1 and outer radius rb2. The inner sphere carries a charge Q while the outer sphere does not

carry any net charge.

33. The electric field in a region is given by r

r

kQE ˆ

2

where Q is the charge. What is the potential

between r = a to r = b?

C)

abkQ

11

30. The electric field for ra r rb1 is

B) kQ/r2

31. The electric field for rb1 r rb2 is

E) zero

32. The electric field for r rb1 is

B) kQ/r2

Use the following to answer the next three questions:

34. Which of the points shown in the diagram are at the same potential?

C) 1 and 4

35. Which point in the electric field in the diagram is at the highest potential?

E) 5

36. Which point in the electric field in the diagram is at the lowest potential?

C) 3 37.

The figure shows two plates A and B. Plate A has a potential of 0 V and plate B a potential of

100 V. The dotted lines represent equipotential lines of 25, 50, and 75 V. A positive test

charge of 1.6 × 10–19 C at point x is transferred to point z. The energy gained or expended by

the test charge is

B) 8 × 10–18 J, expended.

38. The electrostatic potential energy of the system of point charges q1 = 1 µC, q2 = 2 µC, and q3 = 3

µC at the corners of the equilateral triangle whose side s = 30 cm is

D) 0.330 J

39.

Q

R

R

from infinity

Calculate the work done to bring a charge, Q = 1 mC, from infinity and place it at a

distance R = 10 cm along the axis of a thin uniformly charged ring with linear charge

density = 10 C/m and radius R.

D) 399 J