Consider the following configuration of fixed. uniformly charged sphere in a blu

Question

Consider the following configuration of fixed. uniformly charged sphere in a blue sphere fixed at the origin with positive charge q. a red sphere fixed at the point (d_1, 0) with unknown charge and a yellow sphere fixed at the point (d_2 cos (theta), - d_2 sin (theta)) with unknown charge The net electric force on the blue sphere has a magnitude F and is directed in the - y direction What is the sign of the charge on the red sphere? Suppose that the magnitude of the charge on the yellow sphere is determined to be 2q Calculate the charge on the red sphere. Express your answer of q, d_1, d_2, and theta.

Explanation / Answer

C)

use, net force on blue sphere in x-direction = 0

k*q_blue*q_red/d1^2 + k*q_blue*q_yelllo/(d2^2)*cos(theta) = 0

k*q_blue*q_red/d1^2 = - k*q_blue*q_yelllo/(d2^2)*cos(theta)

q*q_red/d1^2 = -q*2*q/(d2^2)*cos(theta)

q_red = -2*q*cos(theta)*(d1/d2)^2

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