Introductory Physics Volume Two

24 Electric Field 1.7
0.5m
+3Q
+Q +2Q
(a) The electric forces on the center charge due to the other two charges
are:
The net force is
F
2Q
Q
F
3Q
F net = F 3Q − F 2Q
= 1
4πɛ 0
=
Q(3Q)
(0.5m) 2 − 1
4πɛ 0
Q(2Q)
(0.5m) 2
(
)
( )
9 × 10 9 N·m2
3 − 2
(1 × 10 −6 C) 2
C 2 (0.5m) 2 = +3.6mN
(b) There are three regions to consider: in between the 2Q and 3Q
charges, outside of these charges to the left and outside of these charges
to the right. Here are force diagrams for placing the charge Q outside
of the two larger charges:
F
3Q
F
3Q
F
2Q
+Q
+3Q
+2Q
+Q
F
2Q
Since the forces point in the same direction, there is no location outside
of the two larger charges where the net electric force on the charge Q
can be zero. For positions inside the two larger charges, the forces will
point in opposite directions, as seen in part (a), and will cancel at the
position where the forces have equal magnitudes. Let’s measure the
location from the+3Q charge:
F
2Q
F 3Q
+3Q
+2Q
The net force on the charge +Q at a position x is
F net = F 3Q − F 2Q
= 1 Q(3Q)
4πɛ 0 x 2 − 1 Q(2Q)
4πɛ 0 (1 − x) 2
x