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Two isolated conducting spheres of radii r₁ and r₂ are charged to the same electric potential. The ratio of the charges on the two spheres, Q₁ Q₂ , is:

Options

  1. Ar₂ r₁
  2. B( r₂ r₁ )^2
  3. Cr₁ r₂
  4. D( r₁ r₂ )^2

Correct answer

C. r₁ r₂

Step-by-step solution

The electric potential at the surface of a conducting sphere of radius r and charge Q is given by V = 1 4 ₀ Q r . Since both spheres are charged to the same potential, we have V₁ = V₂ . 1 4 ₀ Q₁ r₁ = 1 4 ₀ Q₂ r₂ Rearranging the terms gives the ratio of their charges: Q₁ Q₂ = r₁ r₂ Answer: r₁ r₂

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