Magnetic Flux Through An Open Surface
While the magnetic flux through a closed surface is always zero, the magnetic flux through an open surface need not be zero and is an important quantity in electromagnetism. For example, a change in the magnetic flux passing through a loop of conductive wire will cause an electromotive force, and therefore an electric current, in the loop. The relationship is given by Faraday's law:
where
- is the EMF,
- ΦB is the magnetic flux through the open surface Σ,
- ∂Σ is the boundary of the open surface Σ; note that the surface, in general, may be in motion and deforming, and so is generally a function of time. The electromotive force is induced along this boundary.
- dℓ is an infinitesimal vector element of the contour ∂Σ,
- v is the velocity of the boundary ∂Σ,
- E is the electric field,
- B is the magnetic field.
The two equations for the EMF are, firstly, the work per unit charge done against the Lorentz force in moving a test charge around the (possibly moving) surface boundary ∂Σ and, secondly, as the change of magnetic flux through the open surface Σ. This equation is the principle behind an electrical generator.
Read more about this topic: Magnetic Flux
Famous quotes containing the words magnetic, flux, open and/or surface:
“We are in great haste to construct a magnetic telegraph from Maine to Texas; but Maine and Texas, it may be, have nothing important to communicate.”
—Henry David Thoreau (18171862)
“Existence is no more than the precarious attainment of relevance in an intensely mobile flux of past, present, and future.”
—Susan Sontag (b. 1933)
“Thoroughly to unfold the labyrinths of the human mind is an arduous task.... In order to dive into those recesses and lay them open to the reader in a striking and intelligible manner, tis necessary to assume a certain freedom in writing, not strictly perhaps within the limits prescribed by rules.”
—Sarah Fielding (17101768)
“All beauties contain, like all possible phenomena, something eternal and something transitory,something absolute and something particular. Absolute and eternal beauty does not exist, or rather it is only an abstraction skimmed from the common surface of different sorts of beauty. The particular element of each beauty comes from the emotions, and as we each have our own particular emotions, so we have our beauty.”
—Charles Baudelaire (18211867)