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  4. Find the electric flux (in S.I. unit) through the rectangular plate abcd of length l=2 m , width L and whose centre is at a distance OP=x0=(L/2) from an infinite line of charge with linear charge density λ =(1/36 π )× 10- 9 C m- 1 . Consider that the plane of the frame is perpendicular to line OP . <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-lea6fxpvmfyl.png />

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Q. Find the electric flux (in S.I. unit) through the rectangular plate $abcd$ of length $l=2 \, m$ , 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 $OP$ .

Question

NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance

Solution:

Solution
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
$\phi=\frac{\lambda l}{\epsilon _{0}}$
Hence the flux through one plate is
$\phi=\frac{\lambda l}{4 \epsilon _{0}}=0.5$