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Q.

A hollow cylinder has a charge q coulomb within it. If $ϕ$ is the electric flux in units of V-m associated with the curved surface B, the flux linked within the plane surface A is unit of V-m will be

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a

$\frac{q}{ε_{0}} - ϕ$

b

$\frac{q}{2 ε_{0}}$

c

$\frac{ϕ}{3}$

d

$\frac{1}{2} (\frac{q}{ε_{0}} - ϕ)$

answer is D.

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Detailed Solution

Let $ϕ_{A}, ϕ_{B} and ϕ_{c}$ , and are the electric flux linked with A, B and C. According to Gauss theorem,
$\begin{array}{l} ϕ_{A} + ϕ_{B} + ϕ_{c} = \frac{q}{ε_{0}} \sin ce ϕ_{A} = ϕ_{C} \\ ∴ 2 ϕ_{A} + ϕ_{B} = \frac{q}{ε_{0}} \Rightarrow 2 ϕ_{A} = \frac{q}{ε_{0}} - ϕ_{B} \\ \Rightarrow ϕ_{A} = \frac{1}{2} (\frac{q}{ε_{0}} - ϕ) \end{array}$

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