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Question

A cylinder of radius $$R$$ and length $$L$$ is placed in a uniform electric field $$E$$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by :


A
2πR2E
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B
πR2E
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C
RE
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D
Zero
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Solution

The correct option is D Zero
Flux through surface $$A$$,
$${ \phi  }_{ A }=E\times \pi { R }^{ 2 }$$
$${ \phi  }_{ B }=-E\times \pi { R }^{ 2 }$$
Flux through curved surface, $$C=\displaystyle\int { E.ds } $$
                                                   $$=\displaystyle\int { Eds } \cos { { 90 }^{ o } } =0$$
$$\therefore $$ Total flux through cylinder $$={ \phi  }_{ A }+{ \phi  }_{ B }+{ \phi  }_{ C }=0$$
678847_639210_ans_1193eddd9bd74843bab81316c8bf7dfa.png

Physics

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