**QUESTION**

Text

Image

The transformer shown in the figure consists of a long wire coincident with the z-axis carrying a current $I=I_{0} \cos (\omega t)$. coupling magnetic energy to a toroidal coil situated in the $x-y$ plane and centered at the origin. The toroidal core uses iron material with relative permeability $\mu_{r}$, around which 100 turns of a tightly wound coil serves to induce a voltage $V_{\text {emf }}$, as shown in the figure. Calculate $V_{\text {emf }}$ for $f=60 \mathrm{~Hz}, \mu_{r}=4000, a=7 \mathrm{~cm}, b=10.5 \mathrm{~cm}, c=3.5 \mathrm{~cm}$, and $I_{0}=30 \mathrm{~A}$. Answer: \[ V_{e m f}=\quad \sin (\quad t) V \]