(a) Definition of mutual inductance and S.I. unit (b) Obtaining the expression for resultant force on the loop (a) Mutual inductance equals the magnetic flux associated with a coil when unit current flows in its neighbouring coil. Alternatively, Mutual inductance equals the induced emf in a coil when the rate of change of current in its neighbouring coil is one ampere/ second. S.I unit: henry $(H)$ or weber/ampere (or any other correct SI unit) (b) Force per unit length between two parallel straight conductors $F = \frac{\mu_0}{4\pi} \; \frac{2 I_1 I_2}{d}$ Force on the part of the loop which is parallel to infinite straight wire and at a distance $x$ from it. $F_1 = \frac{\mu_0}{2\pi} \; \frac{I_1 I_2 a}{x}$ (away from the infinite straight wire) Force on the part of the loop which is at a distance $(x+a)$ from it $F_2 = \frac{\mu_0}{2\pi} \; \frac{I_1 I_2 a}{x+a}$ (towards the infinite straight wire) Net force $\;F = F_1 - F_2$ $\;F = \frac{\mu_0}{2\pi} I_1 I_2 a \left[ \;\frac{1}{x} - \;\frac{1}{x+a} \right]$ $\;F = \frac{\mu_0}{2\pi} \; \frac{I_1 I_2 a^2}{x(x+a)}$ (away from the infinite straight wire)