Two isolated metallic spheres of radii 2 ,cm | vedclass

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(B) The surface charge density $\sigma$ is defined as the charge per unit area,given by $\sigma = \frac{Q}{A} = \frac{Q}{4 \pi r^2}$.Since the charges

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$4: 1$

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(B) The surface charge density $\sigma$ is defined as the charge per unit area,given by $\sigma = \frac{Q}{A} = \frac{Q}{4 \pi r^2}$.Since the charges $Q$ on both spheres are equal,we have $\sigma \propto \frac{1}{r^2}$.Given radii are $r_1 = 2 \,cm$ and $r_2 = 4 \,cm$.The ratio of charge densities is $\frac{\sigma_1}{\sigma_2} = \frac{r_2^2}{r_1^2}$.Substituting the values,$\frac{\sigma_1}{\sigma_2} = \frac{(4)^2}{(2)^2} = \frac{16}{4} = \frac{4}{1}$.Thus,the ratio is $4: 1$.

Two isolated metallic spheres of radii $2 \,cm$ and $4 \,cm$ are given equal charge,then the ratio of charge density on the surfaces of the spheres will be

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