flux

Examples of flux in the following topics:

• Electric Flux

  • Electric flux is the rate of flow of the electric field through a given area.
  • Electric flux is the rate of flow of the electric field through a given area (see ).
  • Electric flux is proportional to the number of electric field lines going through a virtual surface.
  • Thus, the SI base units of electric flux are kg·m3·s−3·A−1.
  • Electric flux visualized.

• Flux

  • The flux is simply the rate that energy passes through an infinitesimal area (imagine a small window).
  • For example, if you have an isotropic source, the flux is constant across a spherical surface centered on the source, so you find that
  • at two radii around the source.Unless there is absorption or scattering between the two radii, E1 = E2 and we obtain the inverse-square law for flux

• 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.
  • First, EMF is directly proportional to the change in flux Δ.
  • The equation for the EMF induced by a change in magnetic flux is
  • The induced EMF produces a current that opposes the change in flux, because a change in flux means a change in energy.
  • This is one aspect of Lenz's law—induction opposes any change in flux.

• Intensity

  • Although the flux is a useful quantity, it cannot encapsulate all of our knowledge about a radiation field.
  • As you move away from the light bulb, your eye receives less flux (F decreases) and the apparent size of the light bulb also decreases (dΩ decreases).
  • The flux is the power per unit area so the tilted surface gets less flux.
  • Here the two intensities are equal but the upper set of rays delivers less flux.

• 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
  • A generic surface, A, can then be broken into infinitesimal elements and the total magnetic flux through the surface is then the surface integral

• Radiative Shocks

  • Again because the momentum flux is conserved, the gas must remain on the chord throughout.
  • As for the case of a detonation, we find that there is a minimum flux that can pass through an isothermal shock and a minimal velocity change.
  • Just above the flux the flow enters the shock slightly supersonically and leaves subsonically.
  • The ratio of the energy flux entering the radiative shock to that leaving is given by
  • For large values of $M_1$ the initial energy flux is much larger than the final energy flux.

• Problems

  • Calculate from the Euler equation and the continuity equation, at what velocity does the flux ($\rho V$) reach its maximum for fluid flowing through a tube of variable cross-sectional area?
  • At which velocities does the flux vanish?

• 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.

• Relation to the flux

  • From the example at the beginning of this section we can deduce the relationship between the flux and the intensity of the light.Radiation that travels perpendicular to a surface delivers more energy to that surface than radiation traveling at an angle.
  • A_1$, so the total flux traveling through the surface is given by a moment of the intensity.
  • If $I$ is constant with respect to angle, there is as much energy traveling from left to right as from right to left, so the net flux vanishes, or more mathematically the mean of $\cos \theta$ vanishes over the sphere.

• 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).