Question

Three point charges A, B, and C sit on the corners of an equilateral triangle with side length 10cm. Each charge has a of magnitude 2.32 x 10-6 C with charge A and C being negative and B being positive, as shown in the diagram below. What is the net force on each of the point charges? Include vector diagrams for each charge in your answer.

Answer 1

Side length $a = 10\, \text{cm} = 0.1 \, \text{m}$

Charge $q = 2.32 \cdot 10^{-6}\, \text{C}$

Force between any pair of charges (black vectors on picture):

$$F = \frac{1}{4\pi\epsilon_0}\frac{q\cdot q}{a^2}=4.84\, \text{N}$$

Net force equals to vector sum of two forces, acting from two athers charges (red vectors on picture). From geometry,

$$F_A =F_C = 2F\cos{60^\circ}=4.84\, \text{N}$$ $$F_B = 2F\cos{30^\circ}=8.39\, \text{N}$$