A hollow cylinder has a charge `qC` within it. If `phi` is the electric flux in unit of voltmeter associated with the curved surface `B` the flux linked with the plance surface `A` in unit of voltmeter will be

Options

A. `(phi)/(3)`
B. `(q)/(2 in_(0))`
C. `(1)/(2) ((q)/(in_(0)) - phi)`
D. `(q)/(in_(0)) - phi`

Answer

C

Explanation

According to Gauss's theorem, `phi_(total) = (q)/(in_(0))`

Let `phi_(A) = phi_(C) = phi_(0)` and `phi_(B) = phi` (given)
As `phi_(total) = phi_(A) + phi_(C) + phi`
`:. (q)/(in_(0)) - phi_(0) + phi_(0) + phi`
`phi_(0) = (1)/(2) ((q)/(in_(0)) - phi)`