Find the mutual inductance between two rectangular loops, shown in the figure.

Explanation

Let current `i` flow in the loop having `oo` by long sides. Consider a segment of width `dx` at a distance `x` as shown flux throuch the regent
`dphi=[(mu_(0)i)/(2pix)-(mu_(0)i)/(2pi(x+a))]b dx`.
`rArr underset(c)overset(c+b)int[(mu_(0)i)/(2pix)-(mu_(0)i)/(2pi(x+a))]b dx=(mu_(0)ib)/(2pi)["ln" (c+b)/c-"ln" (a+b+c)/(a+c)]`.