Flux passing through the shaded surface of a sphere when a point charge q is placed at the center is (radius of the sphere is R)

Options

A. `q/epsilon_0`
B. `q/2epsilon_0`
C. `q/4epsilon_0`
D. zero

Answer

C

Explanation

c. `alpha = 60^@`. Solid angle subtended by BCD is
`omega = 2pi (1-cos alpha) = pi`
Solid angle subtended by ABDE is
`omega_(ABCDE) - omega_(BCD) = 2pi - pi = pi`
Hence, flux through ABDE is
`phi = q/epsilon_0 pi/(4pi) = q/(4epsilon_0)`