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\,{{\varepsilon }_{0}}} $
• B. $ \frac{\lambda }{8\,{{\varepsilon }_{0}}} $
• C. $ \frac{\lambda }{12\,{{\varepsilon }_{0}}} $
• D. $ \frac{\lambda }{4\,{{\varepsilon }_{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 {{\varepsilon }_{0}}}\times \frac{r\pi }{3}\times \frac{\lambda }{r} $ $ =\frac{\lambda }{12{{\varepsilon }_{0}}} $