Question

Two infinitely long parallel wires having linear charge densities λ1 and λ2 respectively are placed at a distance of R metre. The force per unit length on either wire will be.......?

Answer 1

answer : $\frac{\lambda_1\lambda_2}{2\pi\epsilon_0R}$

Electric field due to infinitely long wire of linear charge density $\lambda_1$ at R distance is given by, $E=\frac{\lambda_1}{2\pi\epsilon_0R}$

it is given that , another infinity long wire is placed at R distance parallel to first wire. so, find charge on the wire.

as we know, $Q=\lambda l$, where l is length of wire.

so, charge on 2nd wire, $Q=\lambda_2l$

from formula, F = QE

here, $Q=\lambda_2l$ and $E=\frac{\lambda_1}{2\pi\epsilon_0R}$

so, force experienced by 2nd wire , F = $\frac{\lambda_1\lambda_2l}{2\pi\epsilon_0R}$

hence, force per unit length, $\frac{F}{l}=\frac{\lambda_1\lambda_2}{2\pi\epsilon_0R}$

Answer 2

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