# 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.

$n=LNβ$ Each loop generates a current $I_{eff}$ $I_{eff}=Indz$

### Magnetic Field In current-carrying solenoid

We apply Ampereβs Law, the magnetic field is given by $B=Lu_{0}NIβ$

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

### Inductance with Solenoid

$L=2ΟRu_{0}N_{2}Aβ$