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If the electric field lines is flowing along axis of a cylinder, then the flux of this field through the
cylindrical surface with the axis parallel to the field is [where, r = radius of cylinder] [UP CPMT 2015]

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zero

$\frac{σ}{2 π r ε_{0}}$

$\frac{σ}{2 ε_{0}}$

$\frac{σ}{ε_{0}}$

answer is C.

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Detailed Solution

Assuming the small area $Δ S$ on the cylindrical surface. The normal to this area will be perpendicular to the axis of the cylinder, but the electric field is parallel to axis.

Hence, $Δ ϕ = E \cdot Δ S \cos θ = E \cdot Δ S \cos \frac{π}{2} = 0$

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