You are building a custom inductor using some scrap parts found in the ECE shop. Using an iron core,

you wrap wire around this core $500$ times. When a $120$V RMS $60$ Hz source is connected to your custom

coil, you measure a current of $1$ A RMS$.$ Ignore the resistance of the wire.

a$)$ Find the reluctance of the core

b$)$ You take some measurements of the core and find its length to be $20$ cm and its cross$-$sectional

area to be $5$ cm$2.$ Find the relative permeability of the material, $$