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

`alpha= 60^(@)`
Solid angle subtended by `BCD`,
`omega= 2pi(1-cos alpha)= pi`
Solid angle subtended bu `ABDE`
`omega_((ABCDE))-omega_((BCD))= 2pi-pi= pi`
Hence flux through `ABCDE: phi-(q)/(epsilon_(0))(pi)/(4pi)=(q)/(4 epsilon_(0))`