(a) Define mutual inductance and write its S.I. unit.

(b) A square loop of side carrying a current I₂ is kept at distance x from an infinitely long straight wire carrying a current I₁ as shown in the figure. Obtain the expression for the resultant force acting on the loop.


 

(a) Mutual inductance : It is a property of two coils due to which each coil opposes any change of current flowing in the other.
The mutually induced e.m.f, in one coil produces the opposition in other coil. 
Its SI unit is henry (H).
(b) A square loop of side carrying a current I2 is kept at distance x from an infinitely long straight wire carrying a current I1 as shown in the figure. Obtain the expression for the resultant force acting on the loop.
The resultant magnetic force of sides AB and DC is zero. The force on side AD is repulsive and on side BC is attractive. Since, AD is near the straight wire. So, the net force will be repulsive.
Force on side AD,
${\mathrm{F}}_1=\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}\frac{{\mathrm{I}}_1{\mathrm{I}}_2\mathrm{a}}{\mathrm{x}} (\mathrm{away} \mathrm{from} \mathrm{wire})$
Therefore, resultant force,
$\begin{array}{l}\mathrm{F}={\mathrm{F}}_1-{\mathrm{F}}_2\\ =\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}{\mathrm{I}}_1{\mathrm{I}}_2\mathrm{a}\left(\frac{1}{\mathrm{x}}-\frac{1}{\mathrm{x}+\mathrm{a}}\right)\\ \mathrm{F}=\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}{\mathrm{I}}_1{\mathrm{I}}_2\mathrm{a}\left(\frac{\mathrm{a}}{\mathrm{x}(\mathrm{x}+\mathrm{a})}\right)\\ \mathrm{F}=\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}\times \frac{{\mathrm{I}}_1{\mathrm{I}}_2{\mathrm{a}}^2}{\mathrm{x}(\mathrm{x}+\mathrm{a})},\end{array}$
(away from wire)