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 (1817–1862)
“Sense is a line, the mind is a circle. Sense is like a line which is the flux of a point running out from itself, but intellect like a circle that keeps within itself.”
—Ralph J. Cudworth (1617–1688)
“Technological change defines the horizon of our material world as it shapes the limiting conditions of what is possible and what is barely imaginable. It erodes ... assumptions about the nature of our reality, the “pattern” in which we dwell, and lays open new choices.”
—Shoshana Zuboff (b. 1951)
“If the man who paints only the tree, or flower, or other surface he sees before him were an artist, the king of artists would be the photographer. It is for the artist to do something beyond this: in portrait painting to put on canvas something more than the face the model wears for that one day; to paint the man, in short, as well as his features.”
—James Mcneill Whistler (1834–1903)