PHYS 21 Spring 2011
HW 1 solutions:
1. Of the charge
Q
initially on a tiny sphere, a portion
q
is to be transferred to a second, nearby sphere.
Both spheres can be treated a particles. For what value of
q
/
Q
>0.5 will the electrostatic force between
the two parts have 1/3 of the maximum possible value?
Solutions for textbook version problem
The magnitude of the force of either of the charges on the other is given by
F
q Q
q
r
1
4
0
2
b
g
where
r
is the distance between the charges. We want the value of
q
that maximizes the function
f
(
q
) =
q
(
Q
–
q
). Setting the derivative
/
dF
dq
equal to zero leads to
Q
–
2
q
= 0, or
q
=
Q
/2. Thus,
q
/
Q
= 0.500.
10. In Fig. 2124 four particles form a square with edge length
a
= 2.81 × 10
2
m. The charges
are
q
1
= q
4
= 1.18 × 10
15
C and
q
2
= q
3
= q
. What is q (in Coulombs) if the net electrostatic
force on particle 1 is zero?
Solution:
For ease of presentation (of the computations below) we assume
Q
> 0 and
q
< 0 (although the final
result does not depend on this particular choice).
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 Spring '08
 Hickman
 Charge, Force, Electric charge, central bead

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