Acharge q is distributed uniformly around the perimeter of a ring of radius r. determine the electric potential difference between the point at the center of the ring and a point on its axis at a distance 6r from the center. (use any variable or symbol stated above along with the following as necessary: ke.) δv

Explanation:

The electric potential due to a charge q at a point r distance arway from it is given by

k is called the Coulomb's constant.

For the given ring of radius R, consider a small element of length dl having charge dq, the electric potential due to this element at a distance r is given by

The length of the whole ring is equal to the circumference of the ring,

The charge Q is uniformly distributed around the perimeter of the ring therefore, the charge on the element of the length dl,

The electric potential at the center of the ring:

The electric potential at the center of the ring due to the small element of ring is given by

The electric potential at the center of the ring due to the whole ring is given by

The electric potential at the distance 6R from the center of the ring along its axis:

The distance of the point, which is at 6R distance from the center of the ring, from the small element is

The electric potential at this point due to the small element is given by

The electric potential at this point due to the whole ring is given by

Thus, the electric potential difference between the point at the center of the ring and a point on its axis at a distance 6R from the center is given by

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