question_answer

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

Correct Answer: C

Solution :

                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 \[=\frac{kq}{r}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\times \frac{r\pi }{3}\times \frac{\lambda }{r}\] \[=\frac{\lambda }{12{{\varepsilon }_{0}}}\]