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 \varepsilon_0 Q \times 10^{20}\, volt / m^{-1}$
• B. $ 12 \pi \varepsilon_0 Q \times 10^{22}\, volt / m^{-1}$
• C. $ 4 \pi \varepsilon_0 Q \times 10^{22}\, volt / m^{-1}$
• D. $ 12 \pi \varepsilon_0 Q \times 10^{20}\, volt / m^{-1}$

Answer 1

Answer: (C)

V = $ \frac{1}{ 4 \pi \varepsilon_0} \cdot \frac{ Q}{ r} = Q \cdot 10^{ 11}$ volts ;
$\therefore \frac{1}{r} = 4 \pi \varepsilon_0 \cdot 10^{11}$
E = $ \frac{ potential}{ r} = Q. 10^{11} \times 4 \pi \varepsilon_0 \cdot 10^{11}$
$\Rightarrow E = 4 \pi \varepsilon_0 \cdot Q \cdot 10^{22}$ volt/ m