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, isa)1 : 2 : 3b)1 : 3 : 5c)1 : 4 : 9d)1 : 8 : 18Correct answer is option 'B'. Can you explain this answer?

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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
b)
1 : 3 : 5
c)
1 : 4 : 9
d)
1 : 8 : 18

Correct answer is option 'B'. Can you explain this answer?

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Three concentric metallic spherical shells of radii R, 2R, 3R, are giv...

The charges on the surfaces of the metallic spheres are shown in the diagram. It is given that the surface charge densities on the outer surfaces of the shells are equal.
Therefore

Q₁ + Q₂ = 4π(2R)²k = 4[4πR²x]

⇒ Q₂ = 4[4πR² x] - Q₁

= 4[4πR²x] -4πR²x = 3[4πR²x]
Also Q₁ + Q₂+ Q₃ = 4π(3R)² x = 9[4πR²x]
∴ Q₃ = 9[4πR²x] - Q₁ - Q₂ = 9[4πR²x] - [4πR²x] -3[4πR²x] = 5[4πR²x]

⇒ Q₁ : Q₂ :Q₃ = 1 :3 :5

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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, isa)1 : 2 : 3b)1 : 3 : 5c)1 : 4 : 9d)1 : 8 : 18Correct answer is option 'B'. Can you explain this answer?

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