# Calculate the mutual inductance between two coils when a current of 4 A changing to 8 A in 0.5 s in one coil, induces an emf of 50 mV in the other coil.

(A) $6.25 × 10^{−3}$ (B) $− 12.5 × 10^{−3}$ (C) $− 6.25 × 10^{−3}$ (D) $12.5 × 10^{−3}$

EMF $\varepsilon = M \large\frac{dI}{dt}$
Given $\varepsilon = 50 mV = 50 \times 10^{−3}V$, $I_1 = 4A, I_2 = 8A$ and $dt = 0.5s$,
$\Rightarrow M = \varepsilon \large\frac{dt}{dI}$$= 50 \times 10^{-3} \large\frac{0.5}{8 - 4}$ $= - 6.25 \times 10^{−3}$