A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by : (A) R/E (B) πR2/E (C) 2πR2E (D) Zero

Answer: (D) Zero

We know,

ϕ = E.ds

Flux through surface of one end, ϕa = E×πR2

Flux through surface of opposite end, ϕb = -E×πR2

Flux through curved surface, ϕc = ∫E.ds

= ∫E.ds. cos90°

= 0

Therefore, total flux = ϕa + ϕb + ϕc

= E×πR2 – E×πR2 + 0

= 0

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