Question

The electric potential at a point in free space due to a charge Q coulomb is $Q\times {10}^{11}V$. The electric field at that point is

• A. $12\pi {\epsilon }_{0}Q\times {10}^{22}V{m}^{-1}$
  
• B. $4\pi {\epsilon }_{0}Q\times {10}^{22}V{m}^{-1}$
  
• C. $12\pi {\epsilon }_{0}Q\times {10}^{20}V{m}^{-1}$
  
• D. $4\pi {\epsilon }_{0}Q\times {10}^{20}V{m}^{-1}$
  

Answer 1

The correct option is B $4\pi {\epsilon }_{0}Q\times {10}^{22}V{m}^{-1}$


Here, $V=\frac{Q}{4\pi {ϵ}_{0}r}=Q\times {10}^{11}$
$\therefore 4\pi {ϵ}_{0}r={10}^{-11}...\left(1\right)$
Now, $E=\frac{Q}{4\pi {ϵ}_0{r}^2}=\frac{Q\times 4\pi {ϵ}_0}{(4\pi {ϵ}_{0}r{)}^2}=\frac{Q\times 4\pi {ϵ}_0}{({10}^{-11}{)}^2}$
$=4\pi {ϵ}_{0}Q\times {10}^{22}V{m}^{-1}$ (using (1))