Consider the following configuration of fixed, uniformly charged spheres in (Figure 1) :

a blue sphere fixed at the origin with positive charge q,

a red sphere fixed at the point (d1,0) with unknown charge qred, and

a yellow sphere fixed at the point (d2cos(θ),−d2sin(θ)) with unknown charge qyellow.

The net electric force on the blue sphere has a magnitude F and is directed in the − y direction.

A. Suppose that the magnitude of the charge on the yellow sphere is determined to be 2q. Calculate the charge qred on the red sphere.

Express your answer in terms of q, d1, d2, and θ.

(o'p) d2