Question

. Equal but opposite currents I flow on the top and bottom of two long parallel plates, as shown in the figure. The plates have width w separation d, where d 《 w. out at page find the magnetic field between the two plates. a) Neglecting edge erects. (b) Calculate the magnetic field energy per unit length. (c) Compute the self inductance per unit length.

Answer 1

In the case of an infinity will the magnetic field at a point located at distance r is given by: B = mu_0 I/2 pi r For two long, parallel wiles a distance d apart, the field at will 2 due to 1 is: B = mu_0 I/2 pi d (equal to field at 1 due to 2) Here, since the current are in opposite directions their magnetic fields at the center sum up: Beta^rightarrow_net = mu_0 I/2 pi(d/2) + mu_0 I/2 pi (d/2) = 2 mu_0 I/pi d Magnetic field energy is given by: U = B^2/2 mu_0 (energy density) Thus, magnetic files energy her unit length is: u/l = B^2/2 mu_0 l = 4 mu^2_0 I^2/pi^2 d^2/2 mu_0 l = 2 mu_0 I^2 l/pi^2 d^2 = BIl/pi d Self inductance per unit length is given by: mu_0 d/w