Two spheres A and B of radius ‘a’ and ‘b’ respectively are at same electric potential. The ratio of the surface charge densities of A and B is
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Given electric potential of spheres are same i.e. $V_{A} = V_{B}$
⇒ ⇒ $\frac{1}{4 \pi \epsilon_0} \cdot \frac{Q_1}{a} =$ $\frac{1}{4 \pi \epsilon_0} \cdot \frac{Q_2}{b} \Rightarrow$ $\frac{Q_1}{Q_2} = \frac{a}{b}$ ......(i)
as surface charge density $\sigma = \frac{Q}{4 \pi r^{2}}$
⇒ ⇒ $\frac{\sigma_1}{\sigma_2} = \frac{Q_1}{Q_2} \times \frac{b^2}{a^2} = \frac{a}{b} \times \frac{b^2}{a^2} = \frac{b}{a}$
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