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. (d)
Solution:
- $Q _1=\sigma\left(4 \pi R^{2}\right)=4 \pi \sigma R^{2}$
$$ \begin{aligned} & Q _2=16 \pi \sigma R^{2}-Q _1=12 \pi \sigma R^{2} \\ & Q _3=36 \pi \sigma R^{2}-16 \pi \sigma R^{2}=20 \pi \sigma R^{2} \\ & Q _1: Q _2: Q _3=1: 3: 5 \end{aligned} $$
