Question

Derive an expression for electric potiential at a distance from a charge q

Answer 1

Answer:

hope it is helpful to you

Answer 2

Answer:

final answer

Explanation:

Let +q be an isolated point charge situated in air at O. P is point at distance r from +q

Consider two points A and B at distance x and x+dx from point O.

The potential difference between A and B is, dv = -E dx

$\begin{aligned}&\mathrm{E}=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{x^{2}} \\&\therefore \mathrm{dV}=-\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{x^{2}} \cdot \mathrm{d} x\end{aligned}$

Negative sign indicates the work is done against electric force

Electric potential at point P due to charge +q is total work done in moving unit charge from infinity to that point.

$\mathrm{v}=-\int_{\infty}^{r} \frac{q}{4 \pi \varepsilon_{0} x^{2}} \cdot \mathrm{d} x=\frac{q}{4 \pi \varepsilon_{0} r}$