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Question

(a) Use Gauss's theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density σ (b) An infinitely large thin plane sheet has a uniform surface charge density +σ . Obtain the expression for the amount of work done in bringing a point charge q from infinity. to a point, distant r, in front of the charged plane sheet.

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Solution

(a)

Let electric charge be uniformly distributed over the surface of a thin non- conducting infinite sheet.
Let the surface charge density be σ. According to Gauss theorem : 1E.ds+2E.ds+3E.ds=qϵ01Eds cos0+2Eds cos0+3Eds cos90=qϵ0 1Eds+2Eds =qϵ0 2Eds =qϵ0 2E.S=σSϵ0 E=σ2ϵ0 (b) The electric field due to a uniformly charged infinitely large thin sheet with surface charge density σ is, E=σ2ϵ0 ...(i) The amount of work done in bringing a point charge q from infinity to a point, at a distance r is given by W=rF.dr Where F is the force experienced by charge q. Now, W=qrE.dr [F=Eq]W=qσ2ϵ0rdr [from (i)]W=qσ2ϵ0[r]=

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