Question

Consider the following configuration of fixed, uniformly chargedspheres (see the figure ):

• a blue sphere fixed at the origin with positivecharge ,
• a red sphere fixed at the point $(d_1,\,0)$ with unknowncharge $q_red$ , and
• a yellow sphere fixed at the point $(d_2\cos(\theta),-d_2\sin(\theta))$ with unknowncharge $q_yellow$ .

The net electric force on the blue sphere has amagnitude and is directed in the y direction.

Suppose that the magnitude of the charge on the yellow sphere isdetermined to be . Calculate the charge $q_red$ on the red sphere.

Express your answer in terms of , $d_1$ , $d_2$ , and .