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A hemisphere of radius $\mathrm{R}$ is placed in a uniform electric field $\mathrm{E}$ so that its axis is parallel to the field. Which of the following statement(s) is / are true?
Solution:
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Verified Answer
The correct answers are:
Flux through the curved surface of hemisphere is $\pi R^2 E$., Total flux enclosed is zero
$$
\begin{aligned}
&\quad \text { as } \phi_{\text {in }}=0, \quad \phi_{\text {total }}=0 \\
&\phi_{\text {curved }}+\phi_{\text {flat }}=0 \\
&\phi_{\text {flat }}=-E \times \pi R^2 \\
&\therefore \phi_{\text {curved }}=E \times \pi R^2
\end{aligned}
$$
Also $\Delta \mathrm{V}=-\overrightarrow{\mathrm{E}} \cdot \Delta \overrightarrow{\mathrm{r}}$ for uniform eletrified.
$$
\begin{aligned}
&\text { as } \vec{E} \perp \Delta \vec{r} \\
&\Delta V=0 \\
&W=q \Delta V=0
\end{aligned}
$$
so work is independent of $R$ in moving charge $q$ from $A+B$
\begin{aligned}
&\quad \text { as } \phi_{\text {in }}=0, \quad \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
\end{aligned}
$$
Also $\Delta \mathrm{V}=-\overrightarrow{\mathrm{E}} \cdot \Delta \overrightarrow{\mathrm{r}}$ for uniform eletrified.
$$
\begin{aligned}
&\text { as } \vec{E} \perp \Delta \vec{r} \\
&\Delta V=0 \\
&W=q \Delta V=0
\end{aligned}
$$
so work is independent of $R$ in moving charge $q$ from $A+B$
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