If a conducting sphere of radius is charged. Then the electric field at a distance from the centre of the sphere would be, (V = potential on the surface of the sphere) [2023]

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Solution

Q.
If a conducting sphere of radius $R$ is charged. Then the electric field at a distance $r (r > R)$ from the centre of the sphere would be, (V = potential on the surface of the sphere) [2023]

1 $\frac{r V}{R^{2}}$

2 $\frac{R^{2} V}{r^{3}}$

3 $\frac{R V}{r^{2}}$

4 $\frac{V}{r}$

Ans.
(3)

Consider a sphere of radius $' R'$ and charge $' Q'$ .

Given, $r > R$

Potential, $V = \frac{K Q}{R}$ ...(i)

Electric field, $E = \frac{K Q}{r^{2}}$ ...(ii)

Using value of $Q = \frac{V R}{K}$ in equation (ii),

$E = \frac{K}{r^{2}} \times \frac{V R}{K} = \frac{V R}{r^{2}}$

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