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Question
Calculate potential on the axis of a disc of radius R due to a charge Q uniformly distributed on its surface.
Solution
`σ = Q/(piR^2)`
`dU = 1/(4piε_0) (σ . 2pirdr)/sqrt(r^2 + z^2)`
∴ U = `(piσ)/(4piε_0) int_O^R (2rdr)/sqrt(r^2 + z^2)`
= `(2piσ)/(4piε_0) [sqrt(r^2 + z^2)]_O^R`
= `(2piσ)/(4piε_0) [sqrt(R^2 + z^2) - z]`
= `(2Q)/(4piε_0R^2) [sqrt(R^2 + z^2) - z]`
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