Q. A ring of radius R is having two charges q and 2q distributed on its two half parts. The electric potential at a point on its axis at a distance of 2√2 R from its centre is $ \displaystyle k = \frac{1}{4\pi\epsilon_0}$
(a) 3kq/R
(b) kq/3R
(c) kq/R
(d) kq/√3R
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Ans: (c)
Sol: Total charge on the ring Q = q + 2q = 3q
Electric Potential at a point on the axis of ring is
$ \displaystyle V = k \frac{Q}{\sqrt{R^2 + x^2}}$
$\displaystyle V= \frac{1}{4\pi \epsilon_0} \frac{3q}{\sqrt{(R^2 + (2\sqrt 2 R)^2)}}$
$\displaystyle V = k \frac{3q}{\sqrt{9 R^2}}$
$ \displaystyle V = k \frac{3q}{3 R}$
$ \displaystyle V = k \frac{q}{ R}$