IIT-JEE 2009 · Paper 1 · Physics Q41

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PhysicsSingle correct+3 / -1Question 41 of 60

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 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

1 : 2 : 3

1 : 3 : 5

1 : 4 : 9

1 : 8 : 18

Answer and worked solution

Official answer: B

Charge on each outer surface. By Gauss's law the outer surface of a shell carries all the charge enclosed by it: $Q_1$ , $Q_1+Q_2$ and $Q_1+Q_2+Q_3$ on the shells of radius $R$ , $2R$ , $3R$ .

Equal surface densities.
$\frac{Q_1}{R^2}=\frac{Q_1+Q_2}{4R^2}=\frac{Q_1+Q_2+Q_3}{9R^2}\implies Q_2=3Q_1,\quad Q_3=5Q_1.$

(B) 1 : 3 : 5

Topics:Conductors and charge distribution Electric flux and Gauss's law

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IIT-JEE 2009 · Paper 1, Physics question 41