Electrostatics 3 Question 8
8. Three concentric metallic spherical shells of radii $R, 2 R$ and $3 R$ are given charges $Q_{1}, Q_{2}$ and $Q_{3}$, 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
(2009)
(a) $1: 2: 3$
(b) $1: 3: 5$
(c) $1: 4: 9$
(d) $1: 8: 18$
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Answer:
Correct Answer: 8. (b)
Solution:
- $Q_{1}=\sigma\left(4 \pi R^{2}\right)=4 \pi \sigma R^{2}$
$ \begin{aligned} & Q_{2}=16 \pi \sigma R^{2}-Q_{1}=12 \pi \sigma R^{2} \\ & Q_{3}=36 \pi \sigma R^{2}-16 \pi \sigma R^{2}=20 \pi \sigma R^{2} \\ & Q_{1}: Q_{2}: Q_{3}=1: 3: 5 \end{aligned} $
