Question

The value of electric potential at a distance of 9 cm from the point charge \(4 \times 10^{-7} \, \text{C}\) is
\[ \text{Given} \, \frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \, \text{N m}^2 \text{C}^{-2} \]

• A. \(4 \times 10^2 \, \text{V}\)
• B. \(44.2 \, \text{V}\)
• C. \(4.4 \times 10^5 \, \text{V}\)
• D. \(4 \times 10^5 \, \text{V}\)

Answer 1

The Correct Option is D

Electric potential $V$ due to a point charge $q$ at distance $r$: 

$$ V = \frac{1}{4\pi\epsilon_0} \frac{q}{r} $$

Given values:

$$ \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N m}^2 \text{C}^{-2} $$ $$ q = 4 \times 10^{-7} \, \text{C} $$ $$ r = 9 \, \text{cm} = 0.09 \, \text{m} $$

Calculation:

$$ V = \left(9 \times 10^9 \, \text{N m}^2 \text{C}^{-2}\right) \frac{4 \times 10^{-7} \, \text{C}}{0.09 \, \text{m}} $$

$$ V = \frac{9 \times 4 \times 10^{9-7}}{0.09} = \frac{36 \times 10^2}{9 \times 10^{-2}} $$

$$ V = \frac{36}{9} \times 10^{2-(-2)} = 4 \times 10^4 $$

$$ V = 4 \times 10^4 \, \text{V} $$