Applications of Ampere’s Circuital Law

Magnetic field due to an infinitely long current carrying conductor

consider an infinitely long current carrying conductor POQ carrying current I. Consider a circular loop of radius r around it in the plane.

Then

ΣB.dl = B 2πr

By applying Ampere’s circuital law, 

B 2πr = µ_oI

B = µ_oI/2πr

This gives the magnetic field around an infinitely long straight current carrying conductor.

Magnetic field due to a solenoid

Solenoids and toroids are widely used in motors, generators, toys, fan-windings, transformers, electromagnets, etc. They are used to provide uniform magnetic field.

A solenoid is a straight coil having a large number of loops set in a straight line with a common axis. a current I flowing through a wire, sets up a magnetic field around it. Suppose that the length of the solenoid is L and it has N number of turns.

|B|= µ₀ nI

The direction of the field is along the axis of the solenoid. The solenoid behaves like a bar magnet.