A cube is made from six thin insulating square faces, each square having side 'd' and carrying a uniformly distributed charge of Q. The magnitude of electric flux leaving the sixth face, due to the electric field of other five faces, is `varphi`. The magnitude of electrostatic force on each face of cube is F. Then,

Options

A. `varphi = (5Q)/(6E_0)`
B. `varphi = (Q)/(2E_0)`
C. `F = (2Q^(2))/(E_(0)d^(2))`
D. `F = (Q^(2))/(E_(0)d^(2))`

Answer

B

Explanation

Self leaving flux on each face `= varphi`
`varphi + varphi' = Q/E_(0) implies phi = varphi' = Q/(2E_(0))`
`F = sigma int EdA cos theta = sigma Q/(2E_(0)) = (Q^2)/(2 E_(0)d^(2))`.