Question

Two coils C₁ and C₂ are placed close to each other. The magnetic flux Φ₂ linked with coil C₂ varies with the current I₁ flowing in coil C₁ as shown in the figure. Find

1. The mutual inductance of the arrangement, and
2. The rate of change of current `((dI_1)/(dt))` will induce an emf of 100V in coil C₂.

Answer 1

1. Φ₂ = magnetic flux linked with coil C₂.
   I₁ = current passes in coil C₁.
   Lets no. of turns in coil C₁ be N₁.
   No. of turns in coil C₂ be N₂.
   According to Faraday's law,
   `E_"ind" = (dphi)/(dt)`
   `E_{21} = -N_2(dphi_2)/(dt)`
   `E_21 = -N_2d/dt(vecB . vecA)`
   `N_2phi_2 prop I_1`
   `N_2phi_2 = M_21I_1`
   M₂₁ is called mutual inductance.
   `M_21 = (N_2phi_2)/I_1`
2. Induced emf (E) = `-L(dI)/(dt)`
   `(dI)/(dt) = E/(-L)`
   `(dI_1)/(dt) = -100(1/L)`

Here, L is the inductance of the coil C₂.