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Two charged conducting spheres S₁ and S₂ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S₁ and S₂ spheres are E_ S₁ and E_ S₂ respectively. The value of E_ S₁ E_ S₂ is _______.

Options

  1. A3 2
  2. B2 3
  3. C4 9
  4. D9 4

Correct answer

D. 9 4

Step-by-step solution

When two conducting spheres are connected by a wire, charge flows until their potentials become equal. V₁ = V₂ k Q₁ R₁ = k Q₂ R₂ The electric field on the surface of a conducting sphere is given by E = k Q R^2 , which can be written as E = V R . Since V₁ = V₂ , we have: E_ S₁ R₁ = E_ S₂ R₂ E_ S₁ E_ S₂ = R₂ R₁ Given R₁ = 8 cm and R₂ = 18 cm: E_ S₁ E_ S₂ = 18 8 = 9 4 Answer: 9 4

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