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A point charge sits on the axis of a circle of radius R, a distance a from the centre, with R = a*sqrt(3). If the electric flux through the circular area is phi, find the magnitude of the point charge.

1. sqrt(3) e0 phi
2. 2 e0 phi
3. 4 e0 phi / sqrt(3)
4. 4 e0 phi

Correct answer: 4 e0 phi

Solution

The cap half-angle gives cos(theta) = a/sqrt(a² + 3a²) = a/(2a) = 1/2, so theta = 60 deg. Solid angle = 2pi(1 - cos theta) = 2pi(1/2) = pi, which is 1/4 of 4pi. Thus phi = (1/4)(Q/e0), giving Q = 4 e0 phi.

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