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)

$4 \pi \varepsilon_0 Q \times 10^{22}\, volt / m^{-1}$

Answer 2

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 = $\frac{ potential}{ r} = 10^{11} \times 4 \pi \varepsilon_0 \cdot 10^{11}$ $\Rightarrow E = 4 \pi \varepsilon_0 \cdot Q \cdot 10^{22}$ volt/ m