Three concentric metallic spherical shells of | vedclass

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Question

Given $\sigma_1=\sigma_2=\sigma_3$

$\frac{Q_1}{4 \pi R^2}=\frac{Q_2}{4 \pi 4 R^2}=\frac{Q_3}{4 \pi 9 R^2}=K$

To find $Q _1: Q _2: Q _3$

$K _4

Vedclass · Accepted Answer

$1: 4: 9$

Vedclass · Answer

Given $\sigma_1=\sigma_2=\sigma_3$

$\frac{Q_1}{4 \pi R^2}=\frac{Q_2}{4 \pi 4 R^2}=\frac{Q_3}{4 \pi 9 R^2}=K$

To find $Q _1: Q _2: Q _3$

$K _4 \pi R ^2: K 16 \pi R ^2: K _3 6 \pi R ^2$

$1: 4: 9$

Three concentric metallic spherical shells of radii $R, 2 R, 3 R$, are given charges $Q_1, Q_2, Q_3$, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $Q_1: Q_2: Q_3$, is

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