First slide

Electrostatic potential

Question

A conducting sphere of radius R is charged to a potential of V volts. The electric field at a distance r(>R) from the center of the sphere would be

Easy

A

$\frac{V}{r}$
B

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

$\frac{RV}{r^{2}}$
D

$\frac{rV}{R^{2}}$

Solution

$V = \frac{q}{4 {πE}_{o} R}$
$q = V 4 {πE}_{o} R$
$E = \frac{q}{4 {πE}_{o} r^{2}} (r > R)$
$= \frac{V . 4 {πE}_{o} R}{4 {πE}_{o} r^{2}} = \frac{VR}{r^{2}}$

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