Problems
 Detailed solution is required.
(Solutions)
1.
Four point charges are located on the xyplane as shown in the figure.
Given q = 1 nC,
the xcomponent of the electric field at the origin is:
3 points
a)
18.0 N/C
b)
12.7 N/C
c)
6.4 N/C
d)
9.0 N/C
e)
zero
E =
2
kq
E
x
= 4Ecosθ =
2
2
2
4
kq
=12,72 N/C
2.
Two spheres of radii a and 2a (a < 1m) are centered on the xaxis at x = 0 m and at x =
6 m, as shown. The spheres have equal uniform surface charge densities. Where on the x
axis can a point charge Q be placed so that the net force on it is zero?
3 points
a)
x =
3 m
b)
x = –4 m
c)
x =
8 m
d)
x =
2 m
e)
x = – 2m
q
1
= σ4πa
2
q
2
= σ4π(2a)
2
=4q
1
2
1
E
E
=
2
1
2
1
)
6
(
4
x
kq
x
kq
−
=
2
2
)
6
(
4
1
x
x
−
=
m
x
2
=
⇒
x
y
q (1m, 1m)
q (1m, 1m)
q (1m, 1m)
q (1m, 1m)
a
2a
x
σ
σ
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3.
Two
rods with nonuniform charge densities are located along the x and yaxis as shown
in the figure. The linear charge densities are λ
1
= 3x
2
nC/m and λ
2
= – 4y
2
nC/m. The
magnitude of the electric field at the origin is:
4 points
a)
90 N/C
b)
132 N/C
c)
198 N/C
d)
154 N/C
e)
148 N/C
2
r
dr
k
dE
λ
=
C
N
dx
m
C
n
k
x
dx
k
dE
/
27
3
2
1
1
=
=
=
λ
C
N
C
N
dx
E
/
54
/
2
*
27
27
4
2
1
=
=
=
∫
C
N
dx
m
C
n
k
y
dx
k
dE
/
36
4
2
2
2
=
=
=
λ
C
N
C
N
dy
E
/
144
/
4
*
36
36
6
2
2
=
=
=
∫
C
N
E
E
E
net
/
8
.
153
2
2
2
1
=
+
=
4
.
A sphere of radius 1m and surface charge density σ = 4 μC/m
2
is centered at the origin.
The work done by the electric field on a point charge q = 1 μC that travels from point A to
B is:
4 points
a)
– 77×10
3
J
m
r
A
6
.
3
3
2
2
2
=
+
=
b)
77×10
3
J
m
r
B
24
.
2
1
2
2
2
=
+
=
c)
328×10
3
J
r
A
d)
– 328×10
3
J
r
B
e)
zero
Q=
C
r
6
2
10
16
4
−
×
=
π
π
σ
;
A
A
r
kQ
V
=
B
B
r
kQ
V
=
J
r
r
qkQ
V
V
q
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 Spring '07
 exams
 Physics, Charge, Magnetic Field, Potential difference, Electric charge, F3

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