Charge is distributed uniformly in some space. The net flux passing through the surface of an imaginary cube of side `a` in the space is `phi`. The net flux passing through the surface of an imaginary sphere of radius `a` in the space will be

Options

A. `phi`
B. `3/(4pi) phi`
C. `(2pi)/3 phi`
D. `(4pi)/3` phi

Answer

D

Explanation

flux = `("enclosed charge through closed surface")/epsilon_(0)`
`phi = (rho xx a^(3))/epsilon_(0)`
`phi_(2) = rho xx (4pi a^(3))/(3 epsilon_(0))`
`phi_(2) = phi xx 4/3pi`