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A small square loop of wire of side l is placed inside a large square loop of wire of side L ( L > > I ) . The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to

Options

  1. Al L
  2. Bl 2 L
  3. CL l
  4. DL 2 l

Correct answer

B. l 2 L

Step-by-step solution

Magnetic field produced by a current i in a large square loop at its centre, B ∝ i L Say B = K i L Therefore, Magnetic flux linked with smaller loop, ϕ=B. S ' ϕ = k i L (/ 2 ) Therefore, the mutual inductance M = ϕ i = K l 2 L or M ∝ l 2 L

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