Question

A thin ring of radius Rhas a charge Q non-uniformly distributed on it. The electrostatic potential at the center of the ring will be
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Answer 1

Given:

A thin ring of radius R has a charge Q non-uniformly distributed on it.

To find:

Electrostatic Potential at centre of ring?

Calculation:

Let's consider an elemental part of ring containing charge dq and total charge of ring be Q.

So, potential due to elemental charge will be:

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

Now, integrating on both sides:

$\displaystyle \implies \int dV = \int\dfrac{k(dq)}{r}$

$\displaystyle \implies \int dV = \dfrac{k}{r} \int \: dq$

$\displaystyle \implies V = \dfrac{kQ}{r}$

$\displaystyle \implies V = \dfrac{Q}{4\pi \epsilon_{0}r}$

Hope It Helps