Q. Three concentric metallic spherical shells of radii R, 2R, 3R given charges $\mathcal{Q}_{1},\mathcal{Q}_{2},\mathcal{Q}_{3}$ 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, $\mathcal{Q}_{1}:\mathcal{Q}_{2}:\mathcal{Q}_{3}$ is
A) 1:2:3
B) 1:3:5
C) 1:4:9
D) 1:8:18
Explanation
(b) $\mathcal{Q}_{1} = \sigma\left( 4\pi R^{2} \right) = 4\pi\sigma R^{2}$
$\mathcal{Q}_{2} = 16\pi\sigma R^{2} - \mathcal{Q}_{1} = 12\pi\sigma R^{2}$
$\mathcal{Q}_{3} = 36\pi\sigma R^{2} = 16\pi\sigma R^{2} = 20\pi\sigma R^{2}$
$\mathcal{Q}_{1}:\mathcal{Q}_{2}:\mathcal{Q}_{3} = 1:3:5$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.