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

The correct option is C $\frac{\lambda }{12{ϵ}_0}$>

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