Three point charges - 2.0 mu C, 3.0 mu C and 4.0 mu C lie on the vertices of an

Question

Three point charges - 2.0 mu C, 3.0 mu C and 4.0 mu C lie on the vertices of an equilateral triangle of side 2.0m. How much work has been done to establish this configuration? Charge is supplied to the metal dome of a Van de Graff generator by the belt at the rate of 300 mu C/s when the potential difference between the belt and the dome is 1.25MV. the dome transfers charge to the atmosphere at the same rate, so the 1.25MV potential difference is maintained. What minimum power is needed to drive the moving belt and maintain the 1.25 MV potential difference? (Difficult)Show that the total work needed to assemble a uniformly charged sphere of total charge Q and radius R is given by 3Q^/(20 pi epsilon_0 R)

Explanation / Answer

9.

q1 = - 2 x 10-6 C

q2 = 3 x 10-6 C

q3 = 4 x 10-6 C

r = length of side of triangle = 2 m

work done = electric potential energy of the system

W = k q1 q2/r + k q2 q3/r + k q3 q1 /r

W = k (q1 q2 + q2 q3 + q3 q1)/r

W = (9 x 109) ((- 2 x 10-6) (3 x 10-6) + (3 x 10-6) (4 x 10-6) + (4 x 10-6) (- 2 x 10-6))/(2)

W = - 0.009 J = - 9 mJ

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