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2. Electric Potential and Capacitance
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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
A
$\frac{\lambda }{{4{\varepsilon _0}}}$
B
$\frac{\lambda }{{8{\varepsilon _0}}}$
C
$\frac{\lambda }{{12{\varepsilon _0}}}$
D
$\frac{\lambda }{{16{\varepsilon _0}}}$
Solution
(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}}}$
Standard 12
Physics
