Ampère's law (redirected from Ampère's circuital law)

Ampère's law

Law of electromagnetism that describes mathematically the magnetic force between two electric currents. It was named after A.-M. Ampère, who discovered that such forces exist. If two currents flow in the same direction, the force between the two wires is attractive; if they flow in opposite directions, the force is repulsive. In each case, the force is directly proportional to the currents.

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Ampère's law

A law of electromagnetism which expresses the contribution of a current element of length dl to the magnetic induction (flux density) B at a point near the current. Ampère's law, sometimes called Laplace's law, was derived by A. M. Ampère after a series of experiments during 1820–1825.

Whenever an electric charge is in motion, there is a magnetic field associated with that motion. The flow of charges through a conductor sets up a magnetic field in the surrounding region. Any current may be considered to be broken up into infinitesimal elements of length dl, and each such element contributes to the magnetic induction at every point in the neighborhood. The contribution dB of the element is found to depend upon the current I, the length dl of the element, the distance r of the point P from the current element, and the angle Θ between the current element and the line joining the element of the point P (see illustration). Ampère's law expresses the manner of the dependence by Eq. (1). The field near

(1) 

a current may be calculated by finding the vector sum of the contributions of all the various elements that make up the current.

Graphic representation of Ampère's law

The proportionality factor k depends upon the units used in Eq. (1) and upon the properties of the medium surrounding the current. In the SI system, the factor k is assigned a value of 10^-7 weber/ampere-meters when the current is in empty space. As in other equations associated with electric and magnetic fields, for example Coulomb's law, it is convenient to replace k by a new factor μ₀ related to k as in Eq. (2).

(2) 

This substitution removes the factor 4π from many derived equations in which it would otherwise appear. With this substitution Ampère's law becomes Eq. (3). The factor μ₀ is called the

(3) 

permeability of empty space.

The direction of dB at each point may be described in terms of a right-hand rule. If the current element is grasped by the right hand with the thumb pointing in the direction of the current, the fingers encircle the current in the direction of the magnetic induction.