CHAPTER 23
Problem
57. A proton moving to the right at
3.8
!
10
5
m/s
enters a region where a 56 kN/C electric field points to
the left. (a) How far will the proton get before its speed reaches zero? (b) Describe its subsequent
motion.
Solution
(a) Choose the
x
-axis to the right, in the direction of the proton, so that the electric field is negative to the
left. If the Coulomb force on the proton is the only important one, the acceleration is
a
x
=
e
(
!
E
)
=
m
.
Equation 2-11, with
v
ox
=
3.8
!
10
5
m/s
and
v
x
=
0,
gives a maximum penetration into the field region
of
x
!
x
0
=
!
v
ox
2
=
2
a
x
=
m
v
ox
2
=
2
eE
=
(1.67
!
10
"
27
kg)(3.8
!
10
5
m/s)
2
2(1.6
!
10
"
19
C)(56
!
10
3
N/C)
=
1.35 cm.
(b) The proton then moves to the left, with the same constant acceleration in the field region, until it exits
with the initial velocity reversed.
Problem
65. A dipole with dipole moment 1.5
nC
!
m
is oriented at 30
°
to a 4.0-MN/C electric field. (a) What is the
magnitude of the torque on the dipole? (b) How much work is required to rotate the dipole until it’s
antiparallel to the field?
Solution
(a) The torque on an electric dipole in an external electric field is given by Equation 23-11;
!
=
p
"
E
=
pE
sin
#
=
(1.5 nC
!
m)(4.0 MN/C) sin30
° =
3.0 mN
!
m.
(b) The work done against just
the electric force is equal to the change in the dipole’s potential energy (Equation 23-12);
W
=
!
U
=
(
"
p
#
E
)
f
"
(
"
p
#
E
)
i
=
pE
(cos 30
°
"
cos180
°
)
=
(1.5 nC
#
m)
$
(4.0 MN/C)(1.866)
=
11.2 mJ.
Chapter 24
Problem
17. The electric field at the surface of a uniformly charged sphere of radius 5.0 cm is
90 kN/C.
What
would be the field strength 10 cm from the surface?
Solution
The electric field due to a uniformly charged sphere is like the field of a point charge for points outside the
sphere, i.e.,
E
(
r
)
ª
1
=
r
2
for
r
!
R
.
Thus, at 10 cm from the surface,
r
=
15 cm
and
E
(15 cm)
=
(5
=
15)
2
E
(5 cm)
=
(90 kN/C)
=
9
=
10 kN/C.
Problem
18. A solid sphere 25 cm in radius carries
14
μ
C,
distributed uniformly throughout its volume. Find the
electric field strength (a) 15 cm, (b) 25 cm, and (c) 50 cm from the sphere’s center.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*