Question

A charge of -1.0 µC is located at the origin, a second charge of 3 µC is located at x = 0, y = 0.1 m, and a third charge of 12 µC is located at x = 0.2 m, y = 0. Find the forces that act on each of the three charges.

q = -1.0 µC

+2.7 N î +2.7 N ĵ

q = 3 µC

+ ? N î + ? N ĵ

q = 12 µC

+? N î + ?N ĵ

Answer 1

F = kq1q2/r^2

F12 = 9x10^9 x 1x3x10^-12 / 0.1^2 = 2.7N up = 2.7 j

F13 = 9x10^9 x 1x12 x 10^-12 / 0.2^2 = 2.7N right = 2.7 i

F32 = 9x10^9 x 3x12 x10^-12 /(0.1^2 + 0.2^2) = 6.48N
acting at angle @ = tan^-1(y/x) = tan^-1(0.1/0.2) = 26.56 deg. in fourth quadrant
F32 = 6.48cos26.56 i - 6.48sin26.56 j = 5.8 i - 2.9 j

a)

Force on 1

F12 + F13 = 2.7i + 2.7 j N

b)

Force on 2

-F12 -F32 = -2.7j - 5.8i + 2.9j = -5.8i = 0.2j N

c)

Force on 3

F32 - F13 = 5.8i - 2.9j - 2.7i = 3.1i - 2.9j N