Question

Find the electric flux (in S.I. unit) through the rectangular plate $abcd$ of length $l=2m$ , width $L$ and whose centre is at a distance $OP=x_0=\frac{L}{2}$ from an infinite line of charge with linear charge density $\lambda =\frac{1}{36\pi }\times 10^{-9}C{m}^{-1}$ . Consider that the plane of the frame is perpendicular to line $OP$ .

Answer 1

Answer: 0.5

If we arrange three more rectangular plates (similar to the one which is given) around the wire, then we get a rectangular box open at both ends. We bring two more plates and use them to close this rectangular box. We can see from the figure that we have a symmetric system for which the total flux is
$\varphi =\frac{\lambda l}{{ϵ}_0}$
Hence the flux through one plate is
$\varphi =\frac{\lambda l}{4{ϵ}_0}=0.5$