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Two thin spherical shells made of metal are at a large distance apart. One of radius 10 cm carries a charge of + 0.5 μ C and the other of radius 20 cm carries a charge of + 0.7 μ C . The charge on each, when they are connected by a suitable conducting wire is respectively

Options

  1. A0 . 4 and 0.8 μ C
  2. B+ 0.425 and + 0.85 μ C
  3. C+ 0.5 and + 0.7 μ C
  4. D+ 0.6 and + 0.6 μ C

Correct answer

A. 0 . 4 and 0.8 μ C

Step-by-step solution

Let us assume that the initial charges on the spheres were Q 1 and Q 2 respectively and the final charges on the spheres are q 1 and q 2 . Finally the potential of both the spheres is the same. k q 1 R 1 = k q 2 R 2 ⇒ q 2 = q 1 R 2 R 1 q 1 + q 2 = Q 1 + Q 2 q 1 = R 1 R 1 + R 2 Q 1 + Q 2 ⇒ q 1 = 10 10 + 20 0 . 5 + 0 . 7 = 0 . 4 μC q 2 = R 2 R 1 + R 2 Q 1 + Q 2 ⇒ q 2 = 20 10 + 20 0 . 5 + 0 . 7 = 0 . 8 μC

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