A hollow cylinder has a charge q coulomb within it at the centre. If ϕ is electric flux in units of volt-meter associated with the curved surface B, the flux linked with each of the plane surface A in units of volt-meter will be

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

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$\frac{q}{2 ε_{0}}$

$\frac{ϕ}{3}$

$\frac{q}{ε_{0}} - ϕ$

$\frac{1}{2} (\frac{q}{ε_{0}} - ϕ)$

answer is D.

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Detailed Solution

Total flux through the whole cylinder: $ϕ_{T} = \frac{q}{ε_{0}}$

Flux through two flat surfaces: $ϕ_{F} = \frac{q}{ε_{0}} - ϕ$

Flux through each flat surface: $ϕ'_{F} = \frac{1}{2} (\frac{q}{ε_{0}} - ϕ)$

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