Question

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

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

Answer 1

Answer: (C)

V = $\frac{1}{4\pi {\epsilon }_0}\cdot \frac{Q}{r}=Q\cdot 10^{11}$ volts ;
$\therefore \frac{1}{r}=4\pi {\epsilon }_0\cdot 10^{11}$
E = $\frac{potential}{r}=Q.10^{11}\times 4\pi {\epsilon }_0\cdot 10^{11}$
$\Rightarrow E=4\pi {\epsilon }_0\cdot Q\cdot 10^{22}$ volt/ m