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Question

A square plate of side 'a' is kept below an infinite line charge of charge per unit length λ (as shown in figure). Electric flux associated with the plate is 3λanπϵo tan1(12).
Here, n is

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Solution

ϕnet at a distance 'a' from the wire can be given by :
ϕnet=λaϵo

As it is clear from the diagram that the we have to calculate electric flux for an angular range of 2θ, which can be given by:
ϕ=ϕnet2π.2θ

Now, tan θ=a/2a=12
ϕ=ϕnet2π.2 tan1(12)=λaπϵ0. tan1(12)
Hence, by comparison of the expression given with this, we get n = 3

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