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Consider an imaginary hemispherical surface. A semi – infinite wire of charge density $λ$ is kept with one of its end coinciding with center of hemisphere and wire is kept along the symmetric axis of the hemisphere as shown in the figure. The electric flux through the spherical surface (Curved surface) of the hemisphere is $\frac{n λ R}{4 \in_{0}}$ find n

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answer is 2.

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Detailed Solution

Electric flux through flat surface $\int_{o}^{R} \frac{k λ}{x} (2 π x d x) o_{f} = \frac{λ}{2 \in_{0}} \int_{o}^{R} d x = \frac{λ R}{2 \in_{0}}$

$o_{f} + o_{c} = \frac{λ R}{2 \in_{0}} o_{c u r v e d} = \frac{λ R}{2 \in_{0}}$

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