question_answer

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)  \[\frac{\lambda }{4{{\varepsilon }_{0}}}\]              

B)  \[\frac{\lambda }{8{{\varepsilon }_{0}}}\]

C)  \[\frac{\lambda }{12{{\varepsilon }_{0}}}\]           

D)  \[\frac{\lambda }{16{{\varepsilon }_{0}}}\]  

Correct Answer: C

Solution :

Length of the arc  \[=r\theta =\frac{r\pi }{3}\] Charge on the arc \[=\frac{r\pi }{3}\times \lambda \] \[\therefore \] Potential at centre \[=\frac{kq}{r}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\times \frac{r\pi }{3}\frac{\lambda }{r}=\frac{\lambda }{12{{\varepsilon }_{0}}}\]