Physics $212$ Introduction to Self$-$Inductance and Inductors $3$ To analytically calculate the self$-$inductance of a coil we combine the basic relation for inductors and Faraday$$s Law: $===$ Integrating both sides gives $=$ Usually the flux per coil is very difficult to calculate so inductance is usually measured experimentally. However, the selfinductance of a very long solenoid is easy to find since the magnetic field is uniform inside the solenoid. $4.$ Inductance of a long solenoid: A long thin solenoid has $$ turns, a length $,$ area $$ and a current $.$ a$.$ What is the magnetic flux through one turn of the solenoid? b$.$ Determine the inductance $$ of the solenoid. c$.$ A very long solenoid has $500$ turns, a radius of $2$ and a length of $40$ and a current of $3$A$.$ What is the inductance of the solenoid? d$.$ The coil in an inductor is usually wrapped around an iron core which amplifies the magnetic field. Assume the iron core makes the magnetic field $700$ times larger than without the core. What is the inductance of the