A hollow cylinder has a charge `q C` 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. `(q)/(2 epsilon_(0)) `
B. `(phi)/(3)`
C. `(q )/(epsilon_(0)) - phi`
D. `(1)/(2) ((q)/(epsilon_(0)) - phi )`

Answer

D

Explanation

Let `phi_(A) , phi_(B)` and `phi_(C )` are the electric flux linked with A, Band C.
According to gauss theorem, `phi` total
`= (sum_(q))/(epsilon_(0))`
`phi_(A) + phi_(B) + phi_(C ) + (q)/(epsilon_(0)) `
Since `phi_(A) = phi_(C )`
`:. 2phi_(A) + phi_(B) = (q)/( epsilon_(0))`
or `2 phi_(A) = (q)/(epsilon_(0)) - phi_(B)`
or `2 phi_(A) = (q)/(epsilon_(0)) - phi`
( Given `phi_(B) = phi `)
`:. phi_(A) = (1)/(2) ( (q)/(epsilon_(0)) - phi)`