Answer to Question #87760 in Electricity and Magnetism for Nicholas Legault

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

Consider the arrangement of charges shown on the picture (vector diagram for each charge is also included):

The absolute value of the Coulomb force acting between any pair of charges is:

$$F_1 = \frac{k q^2}{a^2} = \frac{9 \cdot 10^9 \cdot 2.32^2 \cdot 10^{-12}}{10^{-2}} \approx 4.85 \, N$$

Hence, the net forces acting on charges A, B and C are correspondingly defined as follows:

$$F_A = 2 F_1 \cos{60^\circ} = F_1 = 4.85 \, N \\ F_B = 2 F_1 \cos{60^\circ} = F_1 = 4.85 \, N \\ F_C = 2 F_1 \cos{30^\circ} = \sqrt{3} F_1 = 8.40 \,N$$

Answer: 4.85 N, 4.85 N, 8.40 N.