A charge `'q'` is placed on the diagonal `AP` of a cube at a distance `(AP)/(3)` from the point A. Choose the correct option.

Options

A. the sum of electric flux passing through the surfaces `ABCD` and `PQRS` is `(q)/(3epsi_(0))`
B. the sum of electric flux passing through the surfaces `ABCD` and `PQRS` is `(q)/(8epsi_(0))`
C. the flux through both the surfaces `ABCD` and `PQRS` are same
D. the flux through the surfaces `ABCD` is larger than the flux through surfaces `PQRS`.

Explanation

(a) We can easily see that charge q is placed symetrically to surface ABCD, ABSR and ADQR. Charge q is also placed symetrically to rest of the surfaces. If the flux through the surface ABCD is x and through RSPQ is y then the total flux will be 3x + 3y Now by Gauss law Now by Gauss
`(q_("in"))/(epsilon_(0))=phi`
`implies3x+3y=(q)/(epsilon_(0))`
`impliesx+y=(q)/(3epsilon_(0))`
(b). Flux through two surfaces are not same flux via ABCD is larger.