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Question

A uniform electric field E is parallel to the axis of a hollow hemisphere of radius r. The electric flux through the hemispherical surface is

A
πr2E
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B
38πr2E
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C
2πr2E
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D
4πr2E
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Solution

The correct option is A πr2E
Since number of field lines entering from circular side is equal to number of field lines leaving the hemispherical surface, net flux is 0.
ϕnet=0

The total flux through the hemishphere is the sum of the flux through curved surface and circular face.i.e.,
ϕcircular face+ϕcurved surface=0....(1)

Flux through the circular face,ϕcircular face=|E||A|cosθ....(2)

Here, A=πr2 and θ=180

Substituting the values in equation (2), we get
ϕcirular face=πr2Ecos180....(3)

From equation (1) and (3),ϕcurved surface=πr2E

Hence, option (c) is correct answer.

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