Three concentric metallic spherical shells of radii R , 2 R , 3 R are given Q 1 , Q 2 , Q 3 respectively. It is found that the surface charge densities on the outer surfaces of shells are equal. Then,

Question

Three concentric metallic spherical shells of radii R , 2 R , 3 R are given Q 1 , Q 2 , Q 3 respectively. It is found that the surface charge densities on the outer surfaces of shells are equal. Then, the ratio of the charges given to the shells Q 1 : Q 2 : Q 3 is

TestHub · Accepted Answer

Due to induction, net charge on outer surfaces of spheres will be as

$σ = \frac{Q_{1}}{4 π R_{}^{2}} = \frac{Q_{1} + Q_{2}}{4 π {(2 R)}^{2}} = \frac{Q_{1} + Q_{2} + Q_{3}}{4 π {(3 R)}^{2}}$

$\Rightarrow Q_{1} = \frac{Q_{1} + Q_{2}}{4} = \frac{Q_{1} + Q_{2} + Q_{3}}{9}$

On solving, we get

$Q_{2} = 3 Q_{1}$ and $Q_{3} = 5 Q_{1}$

Therefore, $Q_{1} : Q_{2} : Q_{3} = 1 : 3 : 5$

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