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An infinitely large thin plane sheet has...

An infinitely large thin plane sheet has a uniform surface charge density `+sigma`. 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.

Text Solution

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Electric field due to the infinitely large plane sheet = `(sigma)/(2epsilon_0)`
`:.` Work done to bring a point charge q from infinity to a point at a distance `r = q(V_(r)-V_(oo))`
`-q int_(oo)^(r ) Edr = -q int_(oo)^(r ) (sigma)/(2epsilon_0) dr = oo`.
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