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 due to both the line charges through the face is ABCD is λL(k ∈0). The value of k is

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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 due to both the line charges through the face is ABCD is $\frac{λ L}{(k \in_{0})}$ . The value of k is

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answer is 2.

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Detailed Solution

$\begin{array}{l} ϕ = q_{in} / ϵ_{0} = \frac{λL + λL}{E_{0}} = \frac{2 λL}{ϵ_{0}} . \\ Flux through ABCD = \frac{Total flux}{4} = \frac{λL}{2 e_{0}} \\ ∴ K = 2 \end{array}$