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Integral calculus is needed to sum the field for an arbitrary shape current. This results in a more complete law, called Ampere’s law, which relates magnetic field and current in a general way. Ampere’s law in turn is a part of Maxwell’s equations, which give a complete theory of all electromagnetic phenomena.
As you know from a previous section, magnetic field of a long straight wire circulates around the wire in circles with the same magnitude B= μ0I /2πr B = μ 0 I / 2 π r at all points of one circle of radius r. r. Let us denote this magnetic field by B(r). B ( r). The circulation of this magnetic field around a circle is easy to work out.
In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law) [1] relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 published paper "On Physical Lines of Force". [2] .
induction: The generation of an electric current by a varying magnetic field. Faraday’s law of induction: A basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF).
Figure \(\PageIndex{2}\): An Amperian loop that is a circle of radius, \(h\), will allow us to determine the magnetic field at a distance, \(h\), from an infinitely-long current-carrying wire. The circulation of the magnetic field along a circular path of radius, \(h\), is given by:
There are two key laws that describe electromagnetic induction: Faraday's law, due to 19ᵗʰ century physicist Michael Faraday. This relates the rate of change of magnetic flux through a loop to the magnitude of the electro-motive force E. induced in the loop. The relationship is. E = d Φ d t.
A more fundamental law than the Biot-Savart law is Ampere’s Law, which relates magnetic field and current in a general way. In SI units, the integral form of the original Ampere’s circuital law is a line integral of the magnetic field around some closed curve C (arbitrary but must be closed).
