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Question

Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q1, Q2, Q3, 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, Q1:Q2:Q3, is :

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

The correct option is C 1:3:5
In metallic shell , all charge will appear on the outer surface of outer shell and charge inside each is zero.
The charge distributions among the shells will occur in such a way that the charge inside each shell is zero and total charge will appear on the outer surface of outer shell. (shown in fig below)
Let surface density of charges of outer surfaces of each shell is σ.
now, Q1=σ.4πR2,
Q1+Q2=σ.4π(2R)2Q2=σ.4π4R2Q1=σ.4π4R2σ.4πR2
=3(σ.4πR2)
and
Q1+Q2+Q3=σ.4π(3R)2
Q3=σ.4π9R2(Q1+Q2)=σ.4π9R2σ.4π4R2=5(σ.4πR2)
thus, Q1:Q2:Q3=1:3:5

199528_32166_ans.png

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