magnetic flux
(noun) A measure of the strength of a magnetic field in a given area.
Examples of magnetic flux in the following topics:

Induced EMF and Magnetic Flux
 It is a change in the magnetic field flux that results in an electromotive force (or voltage).
 The magnetic flux (often denoted or _{B}) through a surface is the component of the magnetic field passing through that surface.
 In the most general form, magnetic flux is defined as
$\Phi_B = \iint_A \mathbf{B} \cdot d\mathbf A$ .  The magnetic flux (often denoted Φ or Φ_{B}) 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.
 galvanometer (noun) An analog measuring device, denoted by G, that measures current flow using a needle deflection caused by a magnetic field force acting upon a currentcarrying wire.

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 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.
 inductor (noun) A device or circuit component that exhibits significant selfinductance; a device which stores energy in a magnetic field.

Faraday's Law of Induction and Lenz' Law
 The minus in the Faraday's law means that the EMF creates a current I and magnetic field B that oppose the change in flux this is known as Lenz' law.
 Faraday's law states that the EMF induced by a change in magnetic flux depends on the change in flux , time t, and number of turns of coils.
 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
$EMF = N\frac{\Delta \Phi}{\Delta t}$ .  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.
 solenoid (noun) A coil of wire that acts as a magnet when an electric current flows through it.
 electromotive force (noun) (EMF)The voltage generated by a battery or by the magnetic force according to Faraday's Law. It is measured in units of volts, not newtons, and thus, is not actually a force.
 flux (noun) The rate of transfer of energy (or another physical quantity) through a given surface, specifically electric flux or magnetic flux.

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).
 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).
 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.  Maxwell's equations A set of equations describing how electric and magnetic fields are generated and altered by each other and by charges and currents.

Motional EMF
 Faraday's law of induction can be used to calculate the motional EMF when a change in magnetic flux is caused by a moving element in a system.
 Any change in magnetic flux induces an electromotive force (EMF) opposing that changea process known as induction.
 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.
 In this equation, N=1 and the flux Φ=BAcosθ.
 electromotive force (noun) (EMF)The voltage generated by a battery or by the magnetic force according to Faraday's Law. It is measured in units of volts, not newtons, and thus, is not actually a force.
 magnetic flux (noun) A measure of the strength of a magnetic field in a given area.

Maxwell's Equations
 Gauss's law for magnetism states that there are no "magnetic charges" analogous to electric charges, and that magnetic fields are instead generated by magnetic dipoles.
 Maxwell added that a changing electric flux can also generate a magnetic field.
 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
$\nabla \cdot \bf B= 0$ 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.
 flux (noun) A quantitative description of the transfer of a given vector quantity through a surface. In this context, we refer to the electric flux and magnetic flux.

A Quantitative Interpretation of Motional EMF
 The EMF can be calculated from two different points of view: 1) in terms of the magnetic force on moving electrons in a magnetic field, and 2) in terms of the rate of change in magnetic flux.
 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).  The current loop is moving into a stationary magnet.
 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.
 magnetic field (noun) A condition in the space around a magnet or electric current in which there is a detectable magnetic force, and where two magnetic poles are present.

Transformers
 Not only does the iron core trap the magnetic field created by the primary coil, its magnetization increases the field strength.
 Since the input voltage is AC, a timevarying magnetic flux is sent to the secondary, inducing its AC output voltage.
 Faraday's law of induction for the secondary coil gives its induced output voltage V_{s} as:
$V_s = N_s \frac{\Delta \Phi}{\Delta t}$ , where N_{s} is the number of loops in the secondary coil and Δ/Δt is the rate of change of magnetic flux.  The crosssectional area of the coils is the same on either side, as is the magnetic field strength, so /Δt is the same on either side.
 The input primary voltage V_{p} is also related to changing flux by:
$V_p = N_p \frac{\Delta \Phi}{\Delta t}$ .  magnetic flux (noun) A measure of the strength of a magnetic field in a given area.
 Faraday’s law of induction (noun) A basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF).

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.
 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.
 Faraday’s law of induction (noun) A basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF).
 electromotive force (noun) (EMF)The voltage generated by a battery or by the magnetic force according to Faraday's Law. It is measured in units of volts, not newtons, and thus, is not actually a force.

Zeeman Effect and Nuclear Spin
 This is why the quantum number
$m$ uses the letter$m$ ; it stands for "magnetic''.  There are two separate effects the interaction of the magnetic moment of the nucleus with that of the current induced by the electron orbital angular momentum and the interaction between the two magnetic moments themselves.
 The situtation for the intrinsic magnetic moment of the electron is a bit more subtle.
 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$\displaystyle \Phi_\textrm{ Outside} = \int_\textrm{ Outside} {\bf B} \cdot {\bf dA} = \mu \int_R^\infty \frac{1}{r^3} 2\pi r d r = 2\pi\frac{\mu}{R}$ 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
$\displaystyle \Phi_\textrm{ Inside} = \int_\textrm{ Inside} {\bf B}_\textrm{ Inside} \cdot {\bf dA} = {\bar{\bf B}} \pi R^2$ and$\displaystyle {\bar{\bf B}}=2\frac{{\mu}}{R^3}.
 This is why the quantum number