Ampère's law Guide, Meaning , Facts, Information and Description
In physics,
Ampère's law is the magnetic equivalent of
Gauss's law, discovered by
André-Marie Ampère. It relates the circulating
magnetic field in a closed loop to the
electric current passing through the loop:
-
where
- B is the magnetic field
- ds is an infinitesimal element (differential) of the closed loop S
- is the current enclosed by the curve S
- is the permeability of free space
- is the path integral along the loop S
James Clerk Maxwell noticed a logical inconsistency when applying Ampère's law on charging
capacitors, and thus concluded that this law had to be incomplete. To resolve the problem, he came up with the concept of
displacement current and made a generalized version of Ampère's which was incorporated into
Maxwell's equations. The generalized formula is as follows:
where is the
flux of
electric field through the surface.
This Ampère-Maxwell law can also be stated in differential form:
where the second term arises from the displacement current; omitting it yields the differential form of the original Ampère's law.
See also
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