Coil 1 has a self-inductance L₁ and a mutual inductance M with a nearby Coil 2. The current in Coil 1 is increasing at a constant rate of dI₁ dt = +k . For the net induced emf in Coil 1 to be exactly zero, the required rate of change of current in Coil 2, dI₂ dt , must be:

Step-by-step solution

The total magnetic flux linked with coil 1 is: ₁ = L₁ I₁ + M I₂ The induced emf in coil 1 is given by Faraday's law: ₁ = - d ₁ dt = -L₁ dI₁ dt - M dI₂ dt We are given that the net induced emf in coil 1 is zero ( ₁ = 0 ) and dI₁ dt = k . 0 = -L₁ (k) - M dI₂ dt M dI₂ dt = -L₁ k dI₂ dt = - L₁ M k Answer: - L₁ M k