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Question

# A hollow cylinder has a charge q coulomb distributed uniformly within it. If ϕ is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of voltmeter 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)Step 1: Total flux through cylinder using Gauss LawBy Gauss Law, total flux through the cylinder is given by: ϕtotal=qε0 ....(1)Step 2: Flux through plane surface AAs surfaces A & C is symmetrical so ϕA=ϕC ϕtotal= ϕA+ϕB+ϕC=qε0 [Using Equation (1)]Given Flux through curved surface ϕB=ϕSo, 2ϕA+ϕ=qε0 ⇒ ϕA=12(qε0−ϕ)

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