(Solved): A magnetic core is shown in Figure 1. Relative permeability of the core is r=2000. Total numbe ...

A magnetic core is shown in Figure 1. Relative permeability of the core is ${?}_{\mathrm{r}}=2000$. Total number of winding turns in the left winding is ${\mathbf{N}}_{\mathbf{L}}=1000$ and in the right winding is ${\mathbf{N}}_{\mathbf{R}}=500$. Assume that the core cross section is uniform and the length of air-gaps is much smaller than the dimensions of the core cross-section. Calculate the following: a) The magnetomotive force in the core if $i=2\mathrm{A}$. b) The magnetic flux, $?$ and magnetic flux density $B$ in the $1\mathrm{mm}$ air gap if $i=2\mathrm{A}$. c) Self inductance of the left coil from Figure 1. d) Mutual inductance between the left and the right coil from Figure 1. Figure 1: Magnetic core for Question 7