Three concentric metallic spherical shells of radii R , 2 R , 3 R are given charges Q 1 , Q 2 , Q 3 , respectively. It is found that the surface charge densities on the outer surfaces of the she

Question

Three concentric metallic spherical shells of radii R , 2 R , 3 R 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

TestHub · Accepted Answer

Q 1 ​ = σ ( 4 π R 2 ) = 4 πσ R 2 ​ Q 2 ​ = 16 πσ R 2 − Q 1 ​ = 12 πσ R 2 Q 3 ​ = 36 πσ R 2 − 16 πσ R 2 = 20 πσ R 2 Q 1 ​ : Q 2 ​ : Q 3 ​ = 1 : 3 : 5 ​

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