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Question

A cylinder of radius R and length l is placed in a uniform electric field E parallel to the axis of the cylinder. The total flux over the curved surface of the cylinder is

A
Zero
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B
πR2E
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C
2πR2E
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D
EπR2
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Solution

The correct option is A Zero

As the cylinder is closed so, the total flux ϕtotal passing through the flux will be zero.i.e.,
ϕtotal=0

Cylinder have two circular faces A and B and a curved surface as shown in figure. So
ϕtotal=ϕA+ϕB+ϕcurved (1)



For face A:

Electric flux ϕA=EA [θ=180]

For face B:

Electric flux, ϕB=EA [ϕ=0]

So the net electric flux through circular faces,
ϕtotal=ϕcurved+EA+EA=0

Now, from (1), ϕcurved=0

Alternative Method:
Since none of the field lines are actually cutting the curved surface so flux is zero.

Hence, option (a) is correct answer.

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