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JEE Main202131 Aug 2021Morning ShiftPhysicsMagnetic Effects of CurrentActual

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. Find the magnetic field at centre, when a current I passes through coil :

Options

  1. Aμ 0 I 8 a + b a - b
  2. Bμ 0 I 4 ( a - b ) 1 a - 1   b
  3. Cμ 0 I 8 a - b a + b
  4. Dμ 0 I N 2 (   b - a ) log e b a

Correct answer

D. μ 0 I N 2 (   b - a ) log e b a

Step-by-step solution

Recall the formula of the magnitude of the magnetic field in terms of current and permeability in free space, B = ∫ a b μ 0 d N i 2 x = ∫ a b μ 0 N b - a d x i 2 x = μ 0 N i 2 ( b - a ) l n b a .

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