magnetic flux

(noun)

A measure of the strength of a magnetic field in a given area.

Related Terms

Examples of magnetic flux in the following topics:

  • Induced EMF and Magnetic Flux

    • 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:

  • Energy Stored in a Magnetic Field

    • This changing magnetic flux produces an EMF which then drives a current.
    • The resulting magnetic flux is proportional to the current.
    • If the current changes, the change in magnetic flux is proportional to the time-rate 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.

  • Changing Magnetic Flux Produces an Electric Field

    • 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. ) Faraday's law of induction is a basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF).
    • 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 and Lenz' Law

    • 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.

  • Motional EMF

    • As seen in previous Atoms, any change in magnetic flux induces an electromotive force (EMF) opposing that change—a process known as induction.
    • 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.
    • In this equation, N=1 and the flux Φ=BAcosθ.
    • Since the flux is increasing, the induced field is in the opposite direction, or out of the page.

  • Inductance

    • 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.

  • Maxwell's Equations

    • 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 time-varying 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 Quantitative Interpretation of Motional EMF

    • 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).
    • But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet.
    • The current loop is moving into a stationary magnet.
    • The direction of the magnetic field is into the screen.
    • Current loop is stationary, and the magnet is moving.

  • Back EMF, Eddy Currents, and Magnetic Damping

    • 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.
    • As it enters and leaves the field, the change in flux produces an eddy current.
    • Magnetic force on the current loop opposes the motion.

  • Zeeman Effect and Nuclear Spin

    • If we average over the precession of the magnetic moments around the imposed magnetic field we get the following splitting
    • The field of a magnetic dipole is given by
    • 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