Question

CP0158 16. Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density o. They are brought in contact and separated. What will be the new surface charge densities on them? ​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

Let σ be the surface charge on the two metal spheres of radii R and 2 R.

∴ Before contact, charges on the two spheres are

Q1=σ.4πR2,andQ2=σ=σ4π(2R)2=4Q1

When the two spheres are brought in contact, their charges are shared till their potentials become equal. If Q1'andQ2' are the final charges on the two spheres after contact, then as V1=V2

Q'14π∈0R=Q'24π∈0(2R)∴Q2=2Q1' ...(i)

As there is no less of charge in the process, therefore,

Q'1+Q'2=Q1+Q2=Q1+4Q1=5Q1=5(σ4πR2) using (i), Q'1+2Q'1=5σ4πR2

Q'1=53σ4πR2andQ'2=2Q'1=103σ4πR2

Hence σ1=Q'14πR2=53σ and σ2=Q'24π(2R)2=56σ

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