We will summarize the basic equations for the magnetic field and their applications.
The Lorentz force equation defines the force exerted on a particle of charge q moving through a magnetic field B at velocity v.
The Lorentz force equation is used to derive the force exerted on a on a current-carrying wire of length l from a magnetic field B.
The Biot-Savart law defines the magnetic field at a point r created by a particle of charge q moving with velocity v.
The magnetic field a distance d from an infinitely long current-carrying wire with current I created is derived from the Biot-Savart law.
The magnetic field at a point on the z-axis through the center of a current-carrying loop with current I and area A can be written in terms of the magnetic dipole moment μ as shown.
Ampere's law is the magnetic field equivalent of Gauss's law. Ampere's law relates the current enclosed in a closed integral along a paths to the magnetic field B created by the current I.
