P22_044.PDF

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Chapter 22 - 22.44
44. We are looking for a charge q which, when placed at the origin, experiences F net =0,where
F net = F 1 + F 2 + F 3 .
The magnitude of these individual forces are given by Coulomb’s law, Eq. 22-1, and without loss of
generality we assume q> 0. The charges q 1 (+6 µ C), q 2 (
−
4 µ C), and q 3 (unknown), are located on
the + x axis, so that we know F 1 points towards
x , F 2 points towards + x ,and F 3 points towards
x
if q 3 > 0 and points towards + x if q 3 < 0. Therefore, with r 1 =8m, r 2 =16mand r 3 =24m,wehave
−
−
0=
k q 1 q
r 1
+ k |
q
r 2 −
k q 3 q
r 3
.
Simplifying, this becomes
q 3
24 2
where q 3 is now understood to be in µ C. Thus, we obtain q 3 =
8 2 + 4
0=
−
16 2 −
−
45 µ C.
q 2 |
−
6
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