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Q.

Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them?

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a

σ1=53σ,σ2=56σ

b

σ1=56σ,σ2=52σ

c

σ1=52σ,σ2=56σ

d

σ1=52σ,σ2=53σ

answer is A.

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Detailed Solution

Q1=σ4πR12=σ4πR2 Q2=σ4π(2R)2=σ16πR2 After Redistribution of charges Q1'Q2'=R2R⇒Q2'=2Q1' ..(i) Q1'+Q2'=20σπR2  ...(ii) From eq. (i) and (ii) Q1'=203σπR2⇒σ1'=53σQ2'=403σπR2⇒σ2'=56σ
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