Question

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 denisties 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
A. ` 1: 2: 3`
B. ` 1: 3: 5`
C. ` 1: 4:9`
D. ` 1: 8: 18`

Answer 1

Correct Answer - B
Charge `Q_1` on sheet `1` induces a charge `-Q_1` on the iner surace of sheel `2` and a charge `+ Q_1` on its outer surface , so that the total charge on the louter surcace so shell `2` is `(Q_1 +Q_2)` . This charge inducess a charge - `(Q_1 +Q_2)` on the inner surface of shell `3` and a charge si `(Q_1 +Q_2)` on its outer surcace so that the total charge on the outer surface of shell `3` is `(Q_1 +Q_2 +Q_3)` as shown in the figure. Given that `sigma _1 =sigma _2 = sigma_3`
`rArr Q_1 /(4 pui varepsilon_0 R^2)= ((Q_1 +Q_2))/(4pi varepsilon_0) (2R))^@ = ((Q_1 + Q_2 +q_3))/(4 pi varepsilon_0) (3R))`
.
soving we get ` Q_1 = 3 Q_2 = 5 Q_3` .