Question

At the centre of a half ring of radius $R = 10 \, \text{cm}$ and linear charge density $4n \, \text{C m}^{-1}$, the potential is $x \pi \, \text{V}$. The value of $x$ is ______.

Answer 1

Correct Answer: 36

The potential at the center of a half-ring is given by:

\( V = \frac{KQ}{R} \)

where:

• \( Q = \lambda \pi R \)

Substituting:

\( V = \frac{K \lambda \pi R}{R} \)
\( V = K \lambda \pi \)

Given:

• \( K = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2 \),
• \( \lambda = 4 \times 10^{-9} \, \text{C/m} \)

\( V = 9 \times 10^9 \cdot 4 \times 10^{-9} \cdot \pi \) 
\( V = 36\pi \, \text{V} \)

Thus, \( x = 36 \).

Final Answer: \( x = 36 \).