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

Question #87760
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.
1
Expert's answer
2019-04-17T11:15:18-0400

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 \\\\\nF_B = 2 F_1 \\cos{60^\\circ} = F_1 = 4.85 \\, N \\\\\nF_C = 2 F_1 \\cos{30^\\circ} = \\sqrt{3} F_1 = 8.40 \\,N"

Answer: 4.85 N, 4.85 N, 8.40 N.




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