Question

Consider a uniformly charged sphere that has a total charge of $Q$ that has a radius of $R$. What is the electrostatic potential difference, $\Delta V$ , between the centre of the sphere and the surface of the sphere?

• A. $\frac{4k_{e}q}{R}$
  
• B. $\frac{2k_{e}q}{R}$
  
• C. $\frac{k_{e}q}{R}$
  
• D. $\frac{k_{e}q}{2R}$
  

Answer 1

The correct option is D $\frac{k_{e}q}{2R}$

Total charge $=Q$

radius $=R$

Potential difference $=\Delta V$

$\Delta V=\int E.ds$

$=\int \frac{K\theta }{r^2}dr$

$=KQ\int \frac{dr}{r^2}$

$=KQ\int r^{-2}dr$

$=KQ\frac{r^{-2+1}}{-2+1}$

$=-KQ\frac{1}{2r}$ where radius $=R$

$=\frac{-KQ}{2R}$.