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

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: $x = 36$.