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JEE MainPhysicsElectromagnetic Induction

Two nearby coils, 1 and 2, have a mutual inductance M . The self-inductance of coil 1 is L . The currents flowing through them are given as I₁(t) = I₀ ( t) and I₂(t) = I₀ ( t) respectively. The induced emf in coil 1 as a function of time is:

Options

  1. AI₀ [L ( t) - M ( t)]
  2. B-I₀ [L ( t) + M ( t)]
  3. CI₀ [M ( t) - L ( t)]
  4. DI₀ [L ( t) - M ( t)]

Correct answer

C. I₀ [M ( t) - L ( t)]

Step-by-step solution

Total magnetic flux linked with coil 1 is given by: ₁ = L I₁ + M I₂ Substituting the given currents: ₁ = L I₀ ( t) + M I₀ ( t) According to Faraday's law of induction, the induced emf in coil 1 is: ₁ = - d ₁ dt ₁ = - d dt [L I₀ ( t) + M I₀ ( t)] ₁ = -[L I₀ ( t) - M I₀ ( t)] ₁ = I₀ [M ( t) - L ( t)] Answer: I₀ [M ( t) - L ( t)]

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