Problem $3$:

The magnetic core shown below has a thickness of $t=10cm$ :

Determine the following quantities: a$)$ the equivalent reluctance seen by the coil, ${}_{eq},$ if the core material has a permeability of ${}_c=2000{}_0$; b$)$ the equivalent reluctance seen by the coil, $R_{eq},$ if the core material has a permeability of ${}_c=10,000{}_0$; c$)$ the current I needed to maintain a magnetic flux of ${}_B=100Wb$ in the air gap if the core material has a permeability of ${}_c=2000{}_0$; and d$)$ the current Ineeded to maintain a magnetic flux of ${}_B=100Wb$ in the air gap if the core material has a permeability of ${}_c=10,000{}_0.$

Ans: a$)R_{eq}=8\mathrm{.}589{10}^4$ A $*$ turns $\frac{?}{Wb}$; b$)R_{eq}=1\mathrm{.}744{10}^4$ A turns$/$Wb; c$)I=2\mathrm{.}284$ A; d$)I=2\mathrm{.}225$ A$.$