points total) 04 +0 17. (12 points) The large circle in the figure has a radius
ID: 1875398 • Letter: P
Question
points total) 04 +0 17. (12 points) The large circle in the figure has a radius b. The are shown is a part of a smaller circle of radius a and angular size 75 degrees, that shares the same center as the large circle. The are carries a charge +Q uniformly distributed along its length. Two point charges -g are also located a distance a from the center of the large circle (a) (6 points) Find the voltage at the center of the large circle due to the combined effects of the point charges and the charged arc. (b) (6 points) Determine how much charge must be placed on the outer circle to make the total voltage at the center of the circle 0 V.Explanation / Answer
q1 = q
q2 = Q
q3 = ?
potential due to point charges v1 = -k*q/a - k*q/a = -2*k*q/a
potential due to arc V2 = k*q2/a = k*Q/a
net voltage V = V1 + V2 = (k/a)*(Q-2q)
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potential due to point charges v1 = -k*q/a - k*q/a = -2*k*q/a
potential due to arc V2 = k*q2/a = k*Q/a
potential outer circle V3 = k*q3/b
net voltage V = V1 + V2 + V3 = 0
(k/a)*(Q-2q) + kq3/b = 0
q3 = -(Q-2q)*b/a
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