In figure (a), a charge q is placed just outside the centre of a closed hemisphere. In figure (b), the same charge q is placed just inside the centre of the closed hemisphere and in figure (c), the charge is placed at the centre of hemisphere open from the base. Find the electric flux passing through the hemisphere in all the three cases.

Options

A. `0` , `q/epsilon_0` `q/2epsilon_0`
B. `0` , `0` `q/2epsilon_0`
C. `0` , `q/epsilon_0` `0`
D. `0` , `0` `0`

Answer

A

Explanation

a. Given surface is a closed surface. Therefore we can directly apply the result.
`phi=q_"in"/epsilon_0=0` as `q_"in"=0`
b. Again given surface is a closed surface.
Hence, we can directly apply the result.
`phi=q_"in"/epsilon_0=q/epsilon_0` as `q_"in"=q`
c. Given surface is not closed surface. Hence, we cannot apply the directly result of Gauss's theorem. If we draw a complete sphere, then

`phi` through complete sphere `=q/epsilon_0`
`:. phi` through hemisphere `=1/2(q/epsilon_0)`