PHY108 FALL 08
Solutions for HW2(Due on 9/17)
6. With
x
1
= 6.00 cm and
x
2
= 21.00 cm, the point midway between the two charges is
located at
x
= 13.5 cm. The values of the charge are
q
1
=
–
q
2
=
–
2.00
10
–
7
C, and the
magnitudes and directions of the individual fields are given by:
5
1
1
2
0
1
5
2
2
2
0
1


ˆ
ˆ
i
(3.196 10 N C)i
4
(
)
ˆ
ˆ
i
(3.196 10 N C)i
4
(
)
q
E
x
x
q
E
x
x
Thus, the net electric field is
5
net
1
2
ˆ
(6.39 10 N C)i
E
E
E
7. At points between the charges, the individual electric fields are in the same direction
and do not cancel. Since charge
q
2
=
4.00
q
1
located at
x
2
= 70 cm has a greater
magnitude than
q
1
= 2.1
10
8
C located at
x
1
= 20 cm, a point of zero field must be closer
to
q
1
than to
q
2
. It must be to the left of
q
1
.
Let
x
be the coordinate of
P
, the point where the field vanishes. Then, the total electric
field at
P
is given by
2
1
2
2
0
2
1




1
4
(
)
q
q
E
x
x
x
x
.
If the field is to vanish, then
2
2
1
2
2
2
2
2
2
1
1
1






(
)
.
(
)


q
q
q
x
x
x
x
q
x
x
x
x
Taking the square root of both sides, noting that 
q
2
/
q
1
 = 4, we obtain
70
2.0
20
x
x
.
Choosing
–
2.0 for consistency, the value of
x
is found to be
x
=
30 cm.
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11. The
x
component of the electric field at the center of the square is given by
3
1
2
4
2
2
2
2
0
1
2
3
4
2
0








1
cos45
4
(
/
2)
(
/
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 Spring '08
 IASHVILI
 Physics, Charge, Electric charge, net electric field, Enet

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