Question

A Conducting solid sphere of radius R has total charge Q on it. The electric potential at a point at a distance r from centre varies as(r Options:
1. r⁰
2. 1/r
3. 1/r²
4. 1/r³
Please send ne correct answer
Urgent
Correct answer = brainliest

Answer 1

Given:

A Conducting solid sphere of radius R has total charge Q on it.

To find:

Electric potential at distance r from centre

Calculation:

First of all, the question has clearly mentioned about a CONDUCTING SOLID SPHERE, so we will do as follows:

When r > R (R - radius of sphere)

$\rm \displaystyle\int_{0}^{V} dV = - \int_{ \infty}^{r} E \: dr$

$\rm \implies\displaystyle\int_{0}^{V} dV = \int_{ r}^{ \infty} E \: dr$

$\rm \implies\displaystyle V - 0 = \int_{ r}^{ \infty} E \: dr$

$\rm \implies\displaystyle V = \int_{ r}^{ \infty} E \: dr$

$\rm \implies\displaystyle V = \int_{ r}^{ \infty} \dfrac{kq}{ {r}^{2} } \: dr$

$\rm \implies\displaystyle V = kq\int_{ r}^{ \infty} \dfrac{1}{ {r}^{2} } \: dr$

$\rm \implies\displaystyle V = kq \bigg \{ \frac{ - 1}{r} \bigg \}_{ r}^{ \infty}$

$\rm \implies\displaystyle V = kq \bigg \{ \frac{ 1}{r} \bigg \}_{ \infty}^{r}$

$\rm \implies\displaystyle V = kq \bigg \{ \frac{ 1}{r} - \frac{1}{ \infty} \bigg \}$

$\rm \implies\displaystyle V = kq \bigg \{ \frac{ 1}{r} - 0\bigg \}$

$\rm \implies\displaystyle V = \frac{kq}{r}$

$\rm \implies\displaystyle V = \frac{q}{4\pi \epsilon_{0}r}$

$\rm \implies\displaystyle V \propto \frac{1}{r}$

So, OPTION 2) IS CORRECT.