(Solved): Problem 6.15: Emf in a rectangular loop due to a two-wire line current. A very long lossless thin t ...

Problem 6.15: Emf in a rectangular loop due to a two-wire line current. A very long lossless thin two-wire line in air, with distance between axes of conductors equal to 4a, is fed at one end by an ideal current generator of low-frequency time-harmonic current intensity ig(t) = Ig0 cos \omega t, while the other end of the line is short-circuited. A rectangular wire loop of side lengths a and b is placed in the plane of the line, such that its two sides are parallel to the line and the distance of one of the sides from one of the line conductors is a. Neglecting end and propagation effects, i.e., computing the magnetic field of the line as if it were infinitely long and assuming that the line current is the same in every cross section, as well as the magnetic field due to induced current, find the emf induced in the loop for situations in (a) Fig. 6.32(a) and (b) Fig. 6.32(b), respectively. (a) (b) Figure 6.32 Electromagnetic induction in a rectangular loop due to a time-varying current of a thin two-wire line: (a) loop between line conductors and (b) loop on a side of the line; for Problem 6.15.