WBJEE · Physics · Electrostatics

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?

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 \(R\).

Verified Solution

Answer & Solution

Correct Answer

(C) Total flux enclosed is zero

Step-by-step Solution

Detailed explanation

\[ \begin{aligned} &\quad \text { as } \phi_{\text {in }}=0, \quad \phi_{\text {total }}=0 \\ &\phi_{\text {curved }}+\phi_{\text {flat }}=0 \\ &\phi_{\text {flat }}=-E \times \pi R^2 \\ &\therefore \phi_{\text {curved }}=E \times \pi R^2 \end{aligned} \] Also…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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