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Question
Calculate potential on the axis of a ring due to charge Q uniformly distributed along the ring of radius R.
Solution
Let us take point P to be at a distance z from the centre of the ring, as shown in figure. The charge element dq is at a distance z from point P. Therefore, V can be written as
V = `1/(4piε_0) int (dq)/r = 1/(4piε_0) int (dq)/sqrt(z^2 + a^2)`
Since each element dq is at the same distance from point P, so we have net potential
V = `1/(4piε_0) 1/sqrt(z^2 + a^2) int dq = 1/(4piε_0) 1/sqrt(z^2 + a^2) [Q]`
The net electric potential V = `1/(4piε_0) Q/sqrt(z^2 + a^2)`
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