Practice portal › Electric Potential and Capacitance › Electrostatic Potential Energy
Asked in GUJCET 2014 · Energy of a system of charges
Given: charge Q spread over the surface of a sphere of radius R; K = 1/(4πε₀).
Idea: the stored energy equals the work done in charging the sphere, bringing the charge in small amounts dq from infinity.
When the sphere already holds q, its potential is (Kq)/R, so the next dq needs dW = (Kq)/R dq.
U = ∫₀^Q (Kq)/R dq = (KQ²)/(2R).
So U = 1/2(KQ²)/R, the same as (Q²)/(2C) with C = R/K.
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