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# A ring of radius R is having charges $\; q \;and \; 3 q\;$ distributed on its two half parts . The electric potential at a point on the axis $\;\sqrt{3}\;R\;$ from its centre is

$(a)\;\large\frac{3\;k\;q}{R}\qquad(b)\;\large\frac{2\;k\;q}{R}\qquad(c)\;\large\frac{k\;q}{R}\qquad(d)\;None$

Answer : (b) $\;\large\frac{2\;k\;q}{R}$
Explanation : Every point on ring is at a same distance from p
$d=\sqrt{R^2+3R^2}=2R$
$V=\large\frac{k\;q}{2 R}+\large\frac{k\;3\;q}{2R}=\large\frac{2\;k\;q}{R}\;.$
edited Jan 31, 2014 by yamini.v