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Question

# A hollow cylinder has a charge q C within it placed at the centre. If the electric flux associated with the curved surface B is ϕ, the flux linked with the plane surface A will be

A
qϵ0ϕ
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B
12(qϵ0ϕ)
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C
q2ϵ0
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D
ϕ3
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Solution

## The correct option is B 12(qϵ0−ϕ)Given that, The flux associated with the surface B=ϕB=ϕ The total flux (ϕtotal) linked with the cylinder is the sum of the flux through the faces A, B and C. Let the flux through the face A, B and C is ϕA, ϕB and ϕC ϕtotal=ϕA+ϕB+ϕC…(i) The face A and C is symmetric with respect to the charge q, so flux passing through them will be same. ⇒ϕA=ϕC According to Gauss law, ϕtotal=qϵ0 ⇒ϕtotal=2ϕA+ϕB ⇒qϵ0=2ϕA+ϕB ⇒2ϕA=qϵ0−ϕB ⇒ϕA=12(qϵ0−ϕ) Hence, option (b) is correct. Why this question?Tip: The surface located at symmetricposition w.r.t to charge. The chargewill have equal linked flux, because equal number of field lines will bepassing through these surfaces

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