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Understanding Electrostatic Potential

Two concentri...

Question

Two concentric metallic spherical shells of radii $R$ and $2 R$ are given charges $Q_{1}$ and $Q_{2}$ respectively. The surface charge densities on the outer surface of the shells are equal. Determine the ratio $Q_{1} : Q_{2}$ .

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Solution

Let the surface charge is $σ$
So, $\frac{Q_{1}}{Q_{2}} = \frac{4 π R^{2} σ}{4 π (2 R)^{2} σ} = \frac{1}{4}$
So, $Q_{1} : Q_{2} = 1 : 4$

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