Question

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

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

Answer 1

The correct option is D $\frac{\lambda }{12{ϵ}_o}$


Length of the arc, $l=r\theta =r\frac{\pi }{3}$

Charge on the arc, $q=l\lambda =\frac{\pi \lambda r}{3}$

Potential at the centre $=\frac{kq}{r}=\frac{k\pi \lambda r}{3r}$

$=\frac{1}{4\pi {ϵ}_0}\frac{\pi \lambda }{3}=\frac{\lambda }{12{ϵ}_0}$