Q151 / 155 · WBJEE 2022 · Physics

Figure
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?

  • Correct answer
    A
    Flux through the curved surface of hemisphere is $\pi R^2 E$.
  • B
    Flux through the circular surface of hemisphere is $\pi R^2 E$.
  • Correct answer
    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 $R$.

Solution

$$ \begin{aligned} &\quad \text { as } \phi_{\text {in }}=0, \quad \phi_{\text {total }}=0 \\ &\phi_{\text {curved }}+\phi_{\text {flat }}=0 \\ &\phi_{\text {flat }}=-E \times \pi R^2 \\ &\therefore \phi_{\text {curved }}=E \times \pi R^2 \end{aligned} $$ 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 $A+B$

Hence, the correct answer is options: 'A', 'C'.

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