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Two charge metallic spheres are joined by a very thin metal wire. If the radius of the larger sphere is four times that of the smaller sphere, the electric field near the larger sphere is

Options

  1. Atwice that near the smaller sphere
  2. Bquarter of that near the smaller sphere
  3. Csame as that near the smaller sphere
  4. Dhalf of that near smaller sphere

Correct answer

B. quarter of that near the smaller sphere

Step-by-step solution

Since the spheres are joined by a metal wire, their potentials will be same. Let the radius of the smaller sphere be r₁ and the radius of the larger sphere be r₂=4 r₁ the v = 1 4 ₀ q ₁ r ₁ = 1 4 ₀ q ₂ r ₂ q ₂ q ₁ = r ₂ r ₁ The electric field near the surface of spheres are given by aligned & E ₁= 1 4 ₀ q ₁ r ₁^2 and E ₂= 1 4 ₀ q ₂ r ₂^2 & E ₂ E ₁ = q ₂ q ₁ r ₁^2 r ₂^2 = r ₂ r ₁ r ₁^2 r ₂^2 = r ₁ r ₂ = 1 4 aligned

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