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
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(c) Length of the arc $ = r\theta = \frac{{r\pi }}{3}$
Charge on the arc $ = \frac{{r\pi }}{3} \times \lambda $
$\therefore$ Potential at center $ = \frac{{kq}}{r}$
$ = \frac{1}{{4\pi {\varepsilon _0}}} \times \frac{{r\pi }}{3}\frac{\lambda }{r} = \frac{\lambda }{{12{\varepsilon _0}}}$
Charge on the arc $ = \frac{{r\pi }}{3} \times \lambda $
$\therefore$ Potential at center $ = \frac{{kq}}{r}$
$ = \frac{1}{{4\pi {\varepsilon _0}}} \times \frac{{r\pi }}{3}\frac{\lambda }{r} = \frac{\lambda }{{12{\varepsilon _0}}}$
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