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}$