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.