Examples of magnetic flux in the following topics:



 When a conductor carries a current, a magnetic field surrounding the conductor is produced.
 If the current changes, the change in magnetic flux is proportional to the timerate of change in current by a factor called inductance (L).
 Since nature abhors rapid change, a voltage (electromotive force, EMF) produced in the conductor opposes the change in current, which is also proportional to the change in magnetic flux.
 Thus, inductors oppose change in current by producing a voltage that,in turn, creates a current to oppose the change in magnetic flux; the voltage is proportional to the change in current.
 Express energy stored in a magnetic field in a form of equation




 The picture is similar to the spinorbit coupling except we are looking at the interaction of the total magnetic moment of the atom with the magnetic field
 If we average over the precession of the magnetic moments around the imposed magnetic field we get the following splitting
 Let's imagine that the magnetic moment of the electron is produced by a small ring of current of radius $R$ and integrate the total magnetic flux passing outside the ring through the plane of the ring according the formula above
 and the flux clearly points in a direction opposite to the magnetic moment of the electron.
 Now the total flux through the entire plane that contains the current ring should vanish (the magnetic field is divergence free), so within the ring we have

 Gauss's law for magnetism states that there are no "magnetic charges (or monopoles)" analogous to electric charges, and that magnetic fields are instead generated by magnetic dipoles.
 Thus, the total magnetic flux through a surface surrounding a magnetic dipole is always zero.
 The differential form of Gauss's law for magnetic for magnetism is
 Faraday's law describes how a timevarying magnetic field (or flux) induces an electric field.
 Maxwell added a second source of magnetic fields in his correction: a changing electric field (or flux), which would induce a magnetic field even in the absence of an electrical current.

