1. Fig. 1 shows three situations involving a
charged particle and a uniformly charged
spherical shell. The charges are given,
and the radii of the shells are indicated.
Rank the situations according to the
magnitude of the force on the particle
due to the presence of the shell, greatest
first.
Fig. 1
2. In Fig. 2, four particles form a square. The charges are q1
= q4 = Q and q2 = q3 = q. (a) What is Q/q if the net
electrostatic force on particles 1 and 4 is zero? (b) Is there
any value of q that makes the net electrostatic force on
each of the four particles aero? Explain.
Fig. 2
3. In Fig. 3a, a particle 1 (of charge q1) and
particle 2 (of charge q2) are fixed in
place on an x axis, 8.00 cm apart.
Particle 3 (of charge q3 = ＋6.00×10-19
C) is to be placed on the line between
particles 1 and 2 so that they produce a
Fig. 3
net electrostatic force F3,net on it. Fig. 3b gives the x component of that force
versus the coordinate x at which particle 3 is placed. The scale of the x axis is set
by xs = 8.0 cm. What are (a) the sign of charge q1 and (b) the ratio q2/ q1?
4. Fig. 4 shows two disks and a flat ring, each with
the same uniform charge Q. Rank the objects
according to the magnitude of the electric field
they create at points P (which are at the same
vertical heights), greatest first.
5. Fig. 5 shows an electric dipole. What
are the (a) magnitude and (b) direction
(relative to the positive direction of the
x axis) of the dipole’s electric field at
point P, located at distance r >> d?
Fig. 4
Fig. 5
6. In Fig. 6, a nonconducting rod of length L = 8.15 cm
has a charge －q = –4.23 fC uniformly distributed
along its length. (a) What is the linear charge density
of the rod? What are the (b) magnitude and (c)
Fig. 6
direction (relative to the positive direction of the x
axis) of the electric field produced at point P, at distance a = 12.0 cm from the rod?
What is the electric field magnitude produced at distance a = 50 m by (d) the rod
and (e) a particle of charge –q = –4.23 fC that replaces the rod?
7. In Fig. 7, an electron is shot at an initial speed of v0
= 4.00×106 m/s, at angle 0 = 40.0 from an x axis.
It moves through a uniform electric field
E  (5.00 N / C ) ˆj . A screen for detecting electrons
is positioned parallel to the y axis, at distance x =
3.00 m. In unit-vector notation, what is the velocity
of the electron when it hits the screen?
Fig. 7
8. Fig. 8 shows a closed Gaussian surface in the shape of a cube
of edge length 1.50 m. It lies in a region where the
nonuniform electric field is given by
E  (3.00 x  4.00)iˆ  6.00 ˆj  7.00kˆ N / C , with x in meters.
What is the net charge contained by the cube?
Fig. 8
9. Fig. 9 is a section of a conducting rod of radius R1 = 1.30
mm and length L = 11.00 m inside a thin-walled coaxial
conducting cylindrical shell of radius R2 = 10.0R1 and the
(same) length L. The net charge on the rod is Q1 = +3.40×
10-12 C; that on the shell is Q2 = －2.00Q1. What are the
(a) magnitude E and (b) direction (radially inward or
outward) of the electric field at radial distance r = 2.00R2?
What are (c) E and (d) the direction at r = 5.00R1? What
is the charge on the (e) interior and (f) exterior surface of
the shell?
Fig. 9
10. In Fig. 10, a small, nonconducting ball of mass m = 1.0 mg and
charge q = 2.0×10-8 C (distributed uniformly through its
volume) hangs from an insulating thread that makes an angle 
= 30 with a vertical, uniformly charged nonconducting sheet
(shown in cross section). Considering the gravitational force on
the ball and assuming the sheet extends far vertically and into
and out of the page, calculate the surface charge density  of
the sheet.
Fig. 10
11. Fig. 11 shows two nonconducting spherical shells
fixed in place on an x axis. Shell 1 has uniform
surface charge density ＋5.0 C/m2 on its outer
surface and radius 0.50 cm, and shell 2 has uniform
surface charge density －2.0 C/m2 on its outer
surface and radius 2.0 cm; the centers are separated
by L = 6.0 cm. Other than at x = , where on the x
axis is the net electric field equal to zero?
Fig. 11
12. A spherical drop of water carrying a charge of 30 pC has a potential of 500 V at its
surface (with V = 0 at infinity). (a) What is the radius of the drop? (b) If two such
drops of the same charge and radius combine to form a single spherical drop, what
is the potential at the surface of the new drop?
13. The smiling face of Fig. 12 consists of three items:
(1) a thin rod of charge －3.0 C that forms a full circle of
radius 6.0 cm;
(2) a second thin rod of charge 1.0 C that forms a circular
arc of radius 4.0 cm, subtending an angle of 90 about the
center of the full circle;
(3) an electric dipole with a dipole moment that is
perpendicular to a radial line and has magnitude 1.28×10-21
Cm.
What is the net electric potential at the center?
Fig. 12
14. Fig. 13 shows a thin plastic rod of length L = 13.5
cm and uniform charge 43.6 fC. (a) In terms of
distance d, find an expression for the electric
potential at point P1. (b) Next, substitute variable x
for d and find an expression for the magnitude of
the componet Ex of the electric field at P1. (c) What
is the direction of Ex relative to the positive
Fig. 13
direction of the x axis? (d) What is the value of Ex at
P1 for x = d = 6.60 cm? (e) From the symmetry in Fig. 13, determine Ey at P1.
15. In Fig. 14, a charged particle (either an electron or a
proton) is moving rightward between two parallel
charged plates separated by distance d = 2.00 mm. The
plate potentials are V1 = －70.0 V and V2 = －50.0 V.
The particle is slowing from an initial speed of 90.0 km/s
at the left plate. (a) Is the particle an electron or a proton?
(b) What is its speed just as it reaches plate 2?
Fig. 14
Ans.
1. b and c tie, then a (zero).
2. (a) Q / | q | 2 2 , or Q / q  2 2  2.83. (b) we are unable to construct an
equilibrium configuration with this geometry.
3. (a) positive-valued charge (b) 9.0
4. a, b, c
1 qd
. (b)  j direction
5. (a) | Enet | 
4 0 r 3
6. (a)  = -5.19×10-14 C/m (b) | Ex |  1.57 103 N/C (c) –x direction (d)
| Ex |  1.52 108 N/C (e) | Ex |  1.52 108 N/C

7. v = (3.06  106 m/s) i  (1.71  105 m/s)
8. 8.85  1011 C
9. (a) | E |  0.214 N/C. (b) inward (c) 0.855 N/C (d) outward (e) –3.401012 C
(f) –3.401012 C
10. 5.0×10-9 C/m2
11. 3.9 cm
12. (a) 0.54 mm (b) 790 V
15. (a) proton (b) 65.3 km/s
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