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Two infinite line charges, each having a uniform charge density $λ$ , pass through the midpoints of two pairs of opposite faces of a cube of edge L as shown in figure. The modulus of the total electric flux the in both the line charges through the face is ABCD is $λL / (k \in_{0})$ , find the value of $k$ ?

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answer is 2.

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Detailed Solution

Total flux through the closed surface is $ϕ = \frac{q_{in}}{ϵ_{0}} = \frac{λ L + λ L}{ϵ_{0}} = \frac{2 λ L}{ϵ_{0}}$

Flux through $ABCD = \frac{ϕ_{total}}{4} = \frac{2 λ L}{4 ϵ_{0}} = \frac{λ L}{2 ϵ_{0}}$

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