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JEE Main202329 Jan 2023Morning ShiftPhysicsElectromagnetic InductionActual

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius R is placed inside a large square loop of wire of side L ( L ≫ R ) . The loops are coplanar and their centres coincide :

Options

  1. AM = 2 μ 0 R 2 L
  2. BM = 2 2 μ 0 R L 2
  3. CM = 2 2 μ 0 R 2 L
  4. DM = 2 μ 0 R L 2

Correct answer

C. M = 2 2 μ 0 R 2 L

Step-by-step solution

The magnetic field due to the rectangular loop at its centre is: B = 4 × μ 0 i 4 π L 2 1 2 + 1 2 = 2 2 μ 0 i π L Therefore, the flux through the circular loop ϕ = π R 2 × B = 2 2 μ 0 R 2 i L If M is the mutual inductance, then M d i d t = d ϕ d t = 2 2 μ 0 R 2 L d i d t ⇒ M = 2 2 μ 0 R 2 L

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