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Calculate potential on the axis of a dis...

Calculate potential on the axis of a disc of radius R due to a charge Q uniformly distributed on its surface.

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When a charge Q is distributed uniformly on the surface of a circular disc of radius R, surface charge density
`sigma = (Q)/(pi R^(2))` …(i)
Consider a small element of the circuit disc in the form of a circular strip of radius r and thickness/width dr, Fig 39,
= Area of this element, `q = sigma r dr`
Charge on this element, `q = sigma (2pi r dr)`
Potential due to this element at any point P on the axis of the disc, where `OP = z` is
`dV = (q)/(4pi in_(0) z') = (sigma 2pi r dr)/(4pi in_(0) sqrt(r^(2) + z^(2)))`
Potential at P due to charge on the entire circular disc
`V = (pi sigma)/(4pi in_(0)) int_(0)^(R) (2r dr)/(sqrt(r^(2) + z^(2))) = (2pi sigma)/(4pi in_(0)) [sqrt(r^(2) + z^(2))]_(0)^(R) = (2pi sigma)/(4 pi in_(0)) [sqrt(R^(2) + z^(2)) -z]`
Using (i), `V = (2Q)/(4pi in_(0) R^(2)) [sqrt(R^(2)+ z^(2)) - z]`
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