Two conducting spheres A and B of radius a and $b$ respectively are at the same potential. The ratio

Question

Two conducting spheres A and B of radius a and $b$ respectively are at the same potential. The ratio of the surface charge densities of A and $B$ is\

Professor PC Thomas Classes · Answer

Given the potential of A- potential of B\ ie. $\frac{1}{4 \pi \varepsilon_{0}} \frac{Q_{1}}{a}=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q_{2}}{b}$\ ie., $\frac{Q_{1}}{a}=\frac{Q_{2}}{b} \Rightarrow \frac{4 \pi a^{2} \sigma_{1}}{a}=\frac{4 \pi b^{2} \sigma_{2}}{b}$\ $\Rightarrow \mathrm{a} \sigma_{1}-\mathrm{b} \sigma_{2}$ where $\sigma_{1}$ and $\sigma_{2}$ are the charge densities\ ie. $\frac{\sigma_{1}}{\sigma_{2}}=\frac{b}{a}$.\