8
Some Basic Concepts and Units
Already in 1820, Ampère discovered that a magnetic field is produced by an electrical
charge in motion. He showed that the magnetic field depends on the shape of the circuit
and arrived at the result
which means that the current I in the conductor equals the line integral of H around an
infinitely long rectilinear conductor. Performing the integration along a closed path around
the conductor at a distance r leads to
or
In Chapter 6, we already introduced the force F experienced by a conductor element
carrying a current I in the presence of a magnetic field. In free space, Eq. (6.2) applies:
It can be easily shown from Eqs. (8.3) and (8.4) that if two infinitely long conductors
(carrying currents and are mutually parallel and located at a distance d apart, the
force per length exerted by one conductor on the other equals
Equation (8.5) is used to define the base unit of electric current, the ampere. The equation
contains as a factor the magnetic permeability in vacuum or the magnetic constant For
historical reasons, this factor has been given the numerical value Using this,
one arrives at the famous definition of the ampere: The ampere is that constant electric
current which, if maintained in two straight parallel conductors of infinite length, of negli
gible circular cross-section and placed 1 m apart in vacuum, would produce between these
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