Question

A hemisphere of radius $R$ is placed in a uniform electric field $E$ so that its axis is parallel to the field. Which of the following statement(s) is / are true?

• A. Flux through the curved surface of hemisphere is $\pi R^2 E$.
• B. Flux through the circular surface of hemisphere is $\pi R^2 E$.
• C. Total flux enclosed is zero
• D. Work done in moving a point charge $q$ from $A$ to $B$ via the path $A C B$ depends upon $R$.

Answer 1

Answer: (A), (C)

as $ \varphi_{\text {in }}=0, \varphi_{\text {total }}=0$
$ \varphi_{\text {curved }}+\varphi_{\text {flat }}=0 $
$ \varphi_{\text {flat }}=-E \times \pi R^2 $
$ \therefore \varphi_{\text {curved }}=E \times \pi R^2$
Also $\Delta V=-\vec{E} \cdot \Delta \vec{r}$ for uniform eletrified.
$ \text { as } \vec{E} \perp \Delta \vec{r} $
$\Delta V=0 $
$W=q \Delta V=0$
So work is independent of $R$ in moving charge $q$ from $A+B$