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  • Calculate potential on the axis of a ring due to charge Q uniformly distributed along the ring of radius R.

Calculate potential on the axis of a ring due to charge Q uniformly distributed along the ring of radius R.

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Explanation:-

Given:

  • A ring of radius R with a total charge Q is uniformly distributed along the ring.
  • We are calculating the potential at a point along the axis of the ring, at a distance xxx from the center of the ring.

Here, in the above image, point P is perpendicular to O and is at a distance of z from point O, which is the center of the ring.

The charge dq is at a distance z from the point P.

Therefore, V can be written as:

V=\frac{1}{4\pi \epsilon _{0}}\int \frac{dq}{r}=\frac{1}{4\pi \epsilon _{0}}\int \frac{dq}{\sqrt{z^{2}+a^{2}}}

Since the charge is uniformly distributed, the total charge Q is distributed along the circumference of the ring. The total potential at the point on the axis is the sum of the potentials due to all the small charge elements around the ring. Therefore, the net potential will be :

V=\frac{1}{4\pi \epsilon _{0}}\frac{Q}{\sqrt{z^{2}+a^{2}}}

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