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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:
the physical law that states that the magnetic field around an electric current is proportional to the current; each segment of current produces a magnetic field like that of a long straight wire, and the total field of any shape current is the vector sum of the fields due to each segment
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.
Ampere's Law. The magnetic field in space around an electric current is proportional to the electric current which serves as its source, just as the electric field in space is proportional to the charge which serves as its source. Ampere's Law states that for any closed loop path, the sum of the length elements times the magnetic field in the ...
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] .
Ampere’s Law. 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).
