A solenoid is an inductor which is formed by a helical winding of wire around a cylindrical or toroidal core which may have a magnetic permeability associated with it.
An inductor with inductance L and current I can store magnetic energy
For an infinitely long cylindrical solenoid of radius a (which is a reasonable approximation to a long but finite cylindrical solenoid), the magnetic field is given in cgs by
where I is the current in the wire around the solenoid, N is the number of windings per unit length, c is the speed of light, and
is a unit vector along the axis of the solenoid. The magnetic flux is then
so the inductance is
In MKS
where
is the permeability of free space, so
and
An inductor with inductance L and current I can store magnetic energy
(1)
For an infinitely long cylindrical solenoid of radius a (which is a reasonable approximation to a long but finite cylindrical solenoid), the magnetic field is given in cgs by
(2)
where I is the current in the wire around the solenoid, N is the number of windings per unit length, c is the speed of light, and
is a unit vector along the axis of the solenoid. The magnetic flux is then(3)
so the inductance is
(4)
In MKS
(5)
where
is the permeability of free space, so (6)
and
(7)
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