Three concentric metallic spherical shells of radii $R,\ 2R,3R,$ 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

Question

Dr. Abubacker · Accepted Answer

(b) Due to induction net charges on outer surfaces of spheres are as shown
$\sigma = \frac{Q_{1}}{4\pi R^{2}} = \ \frac{Q_{1} + Q_{2}}{4\pi(2R)^{2}} = \ \frac{Q_{1} + Q_{2} + Q_{3}}{4\pi(3R)^{2}}$
$\Rightarrow Q_{1} = \frac{Q_{1} + Q_{2}}{4} = \ \frac{Q_{1} + Q_{2} + Q_{3}}{9}$
$\Rightarrow Q_{2} = 3Q_{1}$ and $Q_{3} = 5Q_{1}$
$	herefore Q_{1}:Q_{2}:Q_{3} = 1:3:5$

Q. Three concentric metallic spherical shells of radii $R,\ 2R,3R,$ 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

Explanation

Reviewed by Dr. Abubacker

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