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Question

A hollow cylinder has a charge q within it. If ϕ is the electric flux associated with curved surface B. The flux linked with the place 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]According to gauss law,ϕ=Qincε0⟶(1)& from the definition of ϕϕ=E.da⟶(2)For cylindrical surface E.da=2E.{Ar.A}⟶(3)+E.{Ar.B}where {ArA} = Area of surface A.Also, ATQ, E.{ArB}=ϕ1⟶(4)∴ From equ (1), (2), (3) & (4)2E.{Ar.A}+ϕ1=qε0or E.{Ar.A}={qε0−ϕ}12∴ flux through surface area, A, is given by,E.{ArA}=12{qε0−ϕ}∴ Option (B) is the correct answer.

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