Q. An arc of radius $r$ carries charge. The linear density of charge is $\lambda$ and the arc subtends a angle $\frac{\pi}{3}$ at the centre. What is electric potential at the centre
A) $\frac{\lambda}{4\varepsilon_{0}}$
B) $\frac{\lambda}{8\varepsilon_{0}}$
C) $\frac{\lambda}{12\varepsilon_{0}}$
D) $\frac{\lambda}{16\varepsilon_{0}}$
Explanation
(c) Length of the arc $= r\theta = \frac{r\pi}{3}$
Charge on the arc $= \frac{r\pi}{3} \times \lambda$
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$\therefore$ Potential at centre $= \frac{kq}{r}$
$= \frac{1}{4\pi\varepsilon_{0}} \times \frac{r\pi}{3}\frac{\lambda}{r} = \frac{\lambda}{12\varepsilon_{0}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.