Question

An arc of radius $r$ carries charge. The linear density of charge is $\lambda$ and the arc subtends an angle $\frac{\pi}{3}$ at the centre. What is electric potential at the centre?

• A. $\frac{\lambda}{4\epsilon_{0}}$
• B. $\frac{\lambda}{8\epsilon_{0}}$
• C. $\frac{\lambda}{12\epsilon_{0}}$
• D. $\frac{\lambda}{16\epsilon_{0}}$

Answer 1

Answer: (C)

$\frac{\lambda}{12\epsilon_{0}}$

Answer 2

Length of the arc =$r\theta =\frac{r\pi}{3}$
Charge on the are $=\frac{r\pi}{3} \times\lambda$
$\therefore$ Potential at centre $= \frac{kq}{r}$
$=\frac{1}{4 \pi \varepsilon_{0}} \times \frac{r \pi}{3} \frac{\lambda}{r}=\frac{\lambda}{12 \varepsilon_{0}}$