Calculate the mutual inductance of a long straight wire and a rectangular frame with sides `a` and `b`. The frame and the wire lie in the same plan, with the side `b` being closent to the wire, separated by a distance `l` from it and oriented parallel to it.

Explanation

Here, `B = (mu_(0) I)/(2pi r)` at a distance `r` from the wire. The flux through the frame is obtained as,
`Phi_(12) = int_(l)^(a + l) (mu_(0) I)/(2 pi r) bdr = (mu_(0) b)/(2pi) I` In `(1 + (a)/(l))`
Thus, `L_(12) = (Phi_(12))/(I) = (mu_(0) b)/(2pi) In (1 + (a)/(l))`