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A long charged wire is kept on +y axis, with one end at origin. Its linear charge density is given as $λ = λ_{0} y$ . Calculate electric flux passing through the cylinder

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$\frac{λ_{0} L^{2}}{ϵ_{0}}$

$\frac{λ_{0} L^{2}}{2 ϵ_{0}}$

$\frac{2 λ_{0} L}{ϵ_{0}}$

$\frac{2 λ_{0} L^{2}}{ϵ_{0}}$

answer is B.

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Detailed Solution

Charge enclosed $= q = \int_{0}^{L} λdy$

$\int_{0}^{L} (λ_{0} y) dy = λ_{0} (\frac{L_{2}}{2})$

So, $ϕ_{e} = \frac{λ_{0} L^{2}}{2 ϵ_{0}}$

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