Three charges are arranged on a line as shown above. If Q_1 is negative, Q_2 is

Question

Three charges are arranged on a line as shown above. If Q_1 is negative, Q_2 is negative and Q_3 is positive, then O2 MUST feel a net force to the right. If Q_1 is positive, Q_2 is negative and Q_3 is positive, then Q_2 MUST feel a net force to the right. If Q_1 is positive, Q_2 is negative and Q_3 is positive, then Q_2 MIGHT feel a net force to the right. If Q_1 is positive, Q_2 is negative and Q_3 is negative, then Q_2 MUST feel a net force to the right. In the above figure, R = 1.30 m, Q_1 1.73 10^-6 C, Q_2 = Q_1 and Q_3 = Q_1. Calculate the total force on Q_2. Give your answer with a positive number for a force directed to the right. I have been trying to figure out what i am doing wrong for the second question. F = K* ((Q1 * Q2)/R^2). The problem should be (9* 10^9)*(((2.24 * 10^-6)*(2.24 * 10^-6)) (1.10^2) - F. Then multiply this answer by 2. Any thoughts? I'm using the equation listed above and I am still not getting it. Any other advice?

Explanation / Answer

the total charge is equally distibuted on each and every sphere

final charge on each object is Q = (1+9-7-1.6)/4= 0.35 uC

Force on Q2 by Q1 is F12 = k*Q1*Q2/R^2 = (9*10^9*1.73*10^-6*1.73*10^-6)/1.3^2 = 0.01593 N towards Q1 from Q2

Force on Q2 by Q3 is F32 = k*Q3*Q2/R^2 = (9*10^9*1.73*10^-6*1.73*10^-6)/1.3^2 = 0.01593 N towards Q2 from Q3

since the net force direction is left side hence net force has negative sign

si Fnet = -F12-F32 = -2*F12 = -2*0.01593 = -0.03186 N

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