Two isolated charged conducting spheres of radii a and b produce the same electric field near their surfaces . The ratio of electric potential on their surfaces is

$(a)\;\large\frac{a}{b}\qquad(b)\;\large\frac{b}{a}\qquad(c)\;\large\frac{a^2}{b^2}\qquad(d)\;\large\frac{b^2}{a^2}$

Answer : (a) $\;\large\frac{a}{b}$
Explanation : Since electric fields near surfaces are equal
$\large\frac{k\;q_{1}}{a^2}=\large\frac{k\;q^2}{b^2}$
$\large\frac{q_{1}}{q_{2}}=\large\frac{a^2}{b^2}$
The ratio of potential on their surfaces
$\large\frac{k\;q_{1}}{a}\;\large\frac{b}{k\;q_{2}}=\large\frac{q_{1}}{q_{2}}\;\large\frac{b}{a}$
$ratio=\large\frac{a^2}{b^2}\;\large\frac{b}{a}=\large\frac{a}{b}\;.$