Nine different charged balls, which we treat as point charges, are arranged in a

Question

Nine different charged balls, which we treat as point charges, are arranged in a highly symmetric pattern around a square. Note that the value of Q is 4.00 times 10^-5 C, and L = 70.0 cm. What is the magnitude of the net force experienced by the ball with the + Q charge at the center of the square, due to the other 8 charged balls? What is the magnitude of the net force experienced by the ball with the -3Q charge due to the +3Q and +Q charged balls on Use your previous three results to find the magnitude of the net force experienced by the ball with the -3Q charge due to the other 8 charged balls.

Explanation / Answer

a] Most of the forces cancel out each other. Only 3Q and -3Q exert force.

F = 2*3kQ^2/L^2 = 6*9E9*4E-6^2 /0.70^2 = 1.7632 N

b]   F = 3kQ^2/L^2 + 9kQ^2/4L^2= 5.25*9E9*4E-6^2 /0.70^2 = 1.543 N

c] F = kQ^2/L^2 *(3+2.25+12/2 cos 45 degree -30/5*2/sqrt 5 )

= 4.126*9E9*4E-6^2 /0.70^2 = 1.2125 N

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