Consider the following configuration of fixed, uniformly charged spheres in (Fig

Question

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 (d_1,0) with unknown charge q_red, and a yellow sphere fixed at the point {d_2 cos(theta), d_2 sin(theta))with unknown charge q-Yellow 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 yellow sphere? . 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 q_red on the red sphere. Express your answer in terms of q, d_1, d_2, and theta.

Explanation / Answer

force on blue sphere =due to red + due to yellow

Fnet = [ kq qred / d1^2 ](-i) + [ k q qyellow / d2^2] (-cos@i + sin@j)

Fnet = (- kq qred / d1^2 - k q qyellow cos@ / d2^2] i + ( k q qyellow sin@ / d2^2)j

F is directed in the -y axis.

so i component = 0

j component = -ve

( k q qyellow sin@ / d2^2)j = -ve

so q_yellow = -ve charge

yellow sphere negative charged.

and (- kq qred / d1^2 - k q qyellow cos@ / d2^2] = 0

kq qred / d1^2 = - k q qyellow cos@ / d2^2

yellow is negative then red is positive.

qred = - (q_yellow * cos@ * d1^2 / d2^2)

qred = - (2q * cos@ * d1^2 / d2^2) = -2qcos@d1^2 / d2^2

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