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

The electric potential (V) generated by a point charge (q) at a radial distance (r) is calculated using the formula:

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

Constants and given values: $\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N m}^2 \, \text{C}^{-2}$; charge q = 4 × 10^-7 C; distance r = 9 cm, which converts to 0.09 m.

Applying these values to the formula yields: $V = (9 \times 10^9 \, \text{N m}^2 \, \text{C}^{-2}) \frac{(4 \times 10^{-7} \, \text{C})}{0.09 \, \text{m}} = 4 \times 10^4 \, \text{V}$