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. $\frac{\lambda }{4{ϵ}_0}$
• B. $\frac{\lambda }{8{ϵ}_0}$
• C. $\frac{\lambda }{12{ϵ}_0}$
• D. $\frac{\lambda }{16{ϵ}_0}$

Answer 1

Answer: (C)

Length of the arc =$r\theta =\frac{r\pi }{3}$
Charge on the are $=\frac{r\pi }{3}\times \lambda$
$\therefore$ Potential at centre $=\frac{kq}{r}$
$=\frac{1}{4\pi {\epsilon }_0}\times \frac{r\pi }{3}\frac{\lambda }{r}=\frac{\lambda }{12{\epsilon }_0}$