flux density

Examples of flux density in the following topics:

• Ideal Conductors

  • The electric field (Etan) and electric flux density (Dtan) tangential to the surface of a conductor must be equal to 0.
  • This is because any such field or flux that is tangential to the surface of the conductor must also exist inside the conductor, which by definition touches the tangential field or density at one point.
  • Electric flux density normal to the conductor's surface is equal to surface charge density.

• Hydraulic Jump

  • We can define a surface density ${\bar \rho} = \rho h$ and a mean pressure ${\bar p}=\rho g h^2/2$ and recast the equations as
  • Let us examine discontinuities in the fluid height and velocity by using the conditions of continuity on the particle and momentum flux.
  • The mass flux density is simply $j=\rho v h$ and the momentum flux is
  • If we look at the energy flux in the channel we have
  • Because the energy flux of the flow must decrease through the jump $h_2>h_1$ --- the height of the fluid must increase downstream of the jump.

• Radiative Shocks

  • Again because the momentum flux is conserved, the gas must remain on the chord throughout.
  • Just above the flux the flow enters the shock slightly supersonically and leaves subsonically.
  • The initial and final Mach numbers and densities are related through
  • 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.

• B.1 Chapter 1

  • The blackbody flux from the surface of the star is given by
  • The Rosseland mean opacity is related to the density and temperature of the gas through a power-law relationship,
  • The gas is in radiative equilibrium with the radiation field so the flux is constant with respect to $z$ or $\Sigma$.
  • You can see this from the definition of the density of states
  • However, flux is related to the intensity which is energy density times the velocity so the flux is only larger by a factor of $n^2$.

• 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.
  • Therefore, the energy density $u_B = energy / volume$ of a magnetic field B is written as $u_B = \frac{B^2}{2\mu}$.

• The Divergence Theorem

  • More precisely, the divergence theorem states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence over the region inside the surface.
  • The first equation of the Maxwell's equations is often written as $\nabla \cdot \mathbf{E} = \frac {\rho} {\varepsilon_0}$ in a differential form, where $\rho$ is the electric density.
  • The divergence theorem can be used to calculate a flux through a closed surface that fully encloses a volume, like any of the surfaces on the left.
  • It can not directly be used to calculate the flux through surfaces with boundaries, like those on the right.
  • Apply the divergence theorem to evaluate the outward flux of a vector field through a closed surface

• Energy Density

  • To get the total energy density you have to integrate over all of the ray directions
  • Notice how it differs from the flux defined earlier.

• B.11 Chapter 11

  • At which velocities does the flux vanish?
  • where $\rho_0$ is the density at zero velocity.
  • In a more realistic situation, the sound speed is a function of density
  • The flux reaches a maximum of
  • How can we understand this second velocity when the flux vanishes?

• 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