Examples of magnetic flux in the following topics:

 Faraday's law of induction states that an electromotive force is induced by a change in the magnetic flux.
 The magnetic flux (often denoted Φ or ΦB) through a surface is the component of the magnetic field passing through that surface.
 The magnetic flux through some surface is proportional to the number of field lines passing through that surface.
 The magnetic flux passing through a surface of vector area A is
 For a varying magnetic field, we first consider the magnetic flux $d\Phi _B$ through an infinitesimal area element dA, where we may consider the field to be constant:

 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

 We learned the relationship between induced electromotive force (EMF) and magnetic flux.
 In a nutshell, the law states that changing magnetic field $(\frac{d \Phi_B}{dt})$ produces an electric field $(\varepsilon)$, Faraday's law of induction is expressed as $\varepsilon = \frac{\partial \Phi_B}{\partial t}$, where $\varepsilon$ is induced EMF and $\Phi_B$ is magnetic flux.
 The number of turns of coil is included can be incorporated in the magnetic flux, so the factor is optional.
 The magnetic flux is $\Phi_B = \int_S \vec B \cdot d \vec A$, where $\vec A$ is a vector area over a closed surface S.
 But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer (G).

 Faraday's law of induction states that the EMF induced by a change in magnetic flux is $EMF = N\frac{\Delta \Phi}{\Delta t}$, when flux changes by Δ in a time Δt.
 Faraday's experiments showed that the EMF induced by a change in magnetic flux depends on only a few factors.
 The equation for the EMF induced by a change in magnetic flux is
 The minus means that the EMF creates a current I and magnetic field B that oppose the change in flux Δthis is known as Lenz' law.
 (a) When this bar magnet is thrust into the coil, the strength of the magnetic field increases in the coil.

 As seen in previous Atoms, any change in magnetic flux induces an electromotive force (EMF) opposing that change—a process known as induction.
 For example, a magnet moved toward a coil induces an EMF, and a coil moved toward a magnet produces a similar EMF.
 Thus the magnetic flux enclosed by the rails, rod and resistor is increasing.
 When flux changes, an EMF is induced according to Faraday's law of induction.
 Since the flux is increasing, the induced field is in the opposite direction, or out of the page.

 Induction is the process in which an emf is induced by changing magnetic flux, such as a change in the current of a conductor.
 Induction is the process in which an emf is induced by changing magnetic flux.
 In the many cases where the geometry of the devices is fixed, flux is changed by varying current.
 When, for example, current through a coil is increased, the magnetic field and flux also increase, inducing a counter emf, as required by Lenz's law.
 Most devices have a fixed geometry, and so the change in flux is due entirely to the change in current ΔI through the device.

 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.

 A a motional EMF is an electromotive force (EMF) induced by motion relative to a magnetic field B.
 In the case where a conductor loop is moving into magnet shown in (a), magnetic force on a moving charge in the loop is given by $evB$ (Lorentz force, e: electron charge).
 Since the rate of change of the magnetic flux passing through the loop is $B\frac{dA}{dt}$(A: area of the loop that magnetic field pass through), the induced EMF $\varepsilon_{induced} = BLv$ (Eq. 2).
 "...... for example, the reciprocal electrodynamic action of a magnet and a conductor.
 But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet.

 When the coil of a motor is turned, magnetic flux changes, and an electromotive force (EMF), consistent with Faraday's law of induction, is induced.
 As it enters from the left, flux increases, and so an eddy current is set up (Faraday's law) in the counterclockwise direction (Lenz' law), as shown.
 When the metal plate is completely inside the field, there is no eddy current if the field is uniform, since the flux remains constant in this region.
 When a slotted metal plate enters the field, as shown in , an EMF is induced by the change in flux, but it is less effective because the slots limit the size of the current loops.
 As it enters and leaves the field, the change in flux produces an eddy current.