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 $ACB$ depends upon $R$.

Answer 1

Answer: (A), (C)

as ${\phi }_{\text{in }}=0,{\phi }_{\text{total }}=0$
${\phi }_{\text{curved }}+{\phi }_{\text{flat }}=0$
${\phi }_{\text{flat }}=-E\times \pi R^2$
$\therefore {\phi }_{\text{curved }}=E\times \pi R^2$
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 $A+B$