Question

Consider 3 identical conducting loops kept parallel to each other such that their axes coincide. Forloop (1), loop (2) and loop (3) self inductance of each loop is L. Current in loop (1) is I₁, in loop (2) 12 and in loop (3)13, rate of change in current in them at certain instant is $\frac{dl_1}{dt}$, $\frac{dl_2}{dt}$, $\frac{dl_3}{dt}$ respectively. Their mutual inductance is Mᵢⱼ(i.e. for 1 & 2 its M- 12) current in loop (1) and (3) is in same sense and in (2) its in opposite sense:

Answer 1

The question is incomplete.

Answer 2

The problem describes a system of coupled inductors. The induced EMF in each loop depends on the rate of change of current in itself (self-induction) and in the other loops (mutual induction). The magnetic flux linkage and induced EMFs are formulated using the given self and mutual inductances and currents. The total magnetic energy stored in the system is also expressed in terms of self and mutual inductances and currents. The relative direction of currents affects the signs of the mutual inductance terms in the energy expression. Since the question is incomplete, only the foundational equations governing the system are presented.