Question

An arc of radius r carries charge. The linear density of charge is K and the arc subtends an angle of $60{}^{\circ }$ at the centre. What is the value of electric potential at the centre?

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

Answer 1

Answer: (C)

The given situation can be shown as
Length of the arc, $l=r\theta =r\frac{\pi }{3}$ $\therefore$ Charge of the arc $=\frac{r\pi }{3}\times \lambda$ So, the potential at the centre $=\frac{kq}{r}$ $=\frac{1}{4\pi {\epsilon }_0}\times \frac{r\pi }{3}\times \frac{\lambda }{r}$ $=\frac{\lambda }{12{\epsilon }_0}$