Three concentric metallic spherical shells of radii R, 2 R, 3 R are...

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

Three concentric metallic spherical shells of radii R, 2 R, 3 R are given charges Q_1, Q_2, Q_3 , respectively. It is

Options

A $1: 2: 3$
B $1: 3: 5$
C $1: 4: 9$
D $1: 8: 18$

Correct answer

B. $1: 3: 5$

Step-by-step solution

Q_1=\sigma\left(4 \pi R^2\right)=4 \pi \sigma R^2

\begin{aligned}& Q_2=16 \pi \sigmaR^2-Q_1=12 \pi \sigmaR^2 \\ & Q_3=36 \pi \sigmaR^2-16 \pi \sigmaR^2=20 \pi \sigmaR^2 \\ & Q_1: Q_2: Q_3=1: 3: 5 \end{aligned}

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