Force On A Current-carrying Wire
When a wire carrying an electrical current is placed in a magnetic field, each of the moving charges, which comprise the current, experiences the Lorentz force, and together they can create a macroscopic force on the wire (sometimes called the Laplace force). By combining the Lorentz force law above with the definition of electrical current, the following equation results, in the case of a straight, stationary wire:
where ℓ is a vector whose magnitude is the length of wire, and whose direction is along the wire, aligned with the direction of conventional current flow I.
If the wire is not straight but curved, the force on it can be computed by applying this formula to each infinitesimal segment of wire dℓ, then adding up all these forces by integration. Formally, the net force on a stationary, rigid wire carrying a steady current I is
This is the net force. In addition, there will usually be torque, plus other effects if the wire is not perfectly rigid.
One application of this is Ampère's force law, which describes how two current-carrying wires can attract or repel each other, since each experiences a Lorentz force from the other's magnetic field. For more information, see the article: Ampère's force law.
Read more about this topic: Lorentz Force
Famous quotes containing the words force on, force and/or wire:
“If you were to destroy the belief in immortality in mankind, not only love but every living force on which the continuation of all life in the world depended, would dry up at once.”
—Feodor Dostoyevsky (1821–1881)
“‘Tis happy, therefore, that nature breaks the force of all sceptical arguments in time, and keeps them from having any considerable influence on the understanding. Were we to trust entirely to their self-destruction, that can never take place, ‘till they have first subverted all conviction, and have totally destroy’d human reason.”
—David Hume (1711–1776)
“Constantly risking absurdity and death whenever he performs above the heads of his audience the poet like an acrobat climbs on rime to a high wire of his own making.”
—Lawrence Ferlinghetti (b. 1919)