Solenoid

A solenoid is a type of electromagnet formed by a helical coil of wire whose length is substantially greater than its diameter, which generates a controlled magnetic field.

We can use the approximation that each loop in a solenoid is just a circle.

$n=\frac{N}{L}$ Each loop generates a current $I_{eff}$ $I_{eff}=Indz$

Magnetic Field In current-carrying solenoid

We apply Ampere’s Law, the magnetic field is given by $B=\frac{u_{0}NI}{L}$

Derivation#todo $I_{encl}=NI$ $B$

Inductance with Solenoid

$L=\frac{u_0{N}^{2}A}{2\pi R}$