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 densi…

Question

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?

Accepted Answer

Correct answer: D. (d) Before contact, Q_1= 4 R^2 and Q_2= 4 (2R )^2 As, surface charge density, = Netcharge (Q ) Surfacearea (A ) Now, after contact, Q_1^ '+Q_2^ '=Q_1+Q_2=5Q_1=5( 4 R^2) ⋯ (i) They will be at equal potentials, so, Q_1^ 'R= Q_2^ '2R⇒ Q_2^ '=2Q_1^ ' ∴3Q_1^ '=5( 4 R^2) (From equation (i)) and Q_2^ '= 103( 4 R^2) ∴ _1= 53 and _2= 56 .

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

Solution

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