Question

A charge Q is uniformly distributed only on three fourths portion of a ring of radius R. The
electric potential at centre of ring is​

Answer 1

Given:

• Charge Q is distributed on ¾ portion of a ring.

To find:

• Electric potential at centre of ring?

Calculation:

Let's assume that a elemental portion (containing dq charge) of the ring contributes dV electric potential at the centre of the ring.

$\therefore \: dV = \dfrac{k(dq)}{R}$

• 'k' is Coulomb's Constant.

Integrating on both sides with limits:

$\displaystyle \implies \: \int_{0}^{V} dV = \int_{0}^{Q} \dfrac{k(dq)}{R}$

$\displaystyle \implies \: V = \dfrac{kQ}{R}$

$\boxed{ \displaystyle \implies \: V = \dfrac{Q}{4\pi \epsilon_{0}R} }$