Editing Inductance (section)

===Solenoid===
A [[solenoid]] is a long, thin coil; i.e., a coil whose length is much greater than its diameter. Under these conditions, and without any magnetic material used, the [[magnetic field|magnetic flux density]] <math>B</math> within the coil is practically constant and is given by
<math display=block>B = \frac{\mu_0\, N\, i}{\ell}</math>

where <math>\mu_0</math> is the [[magnetic constant]], <math>N</math> the number of turns, <math>i</math> the current and <math>l</math> the length of the coil. Ignoring end effects, the total magnetic flux through the coil is obtained by multiplying the flux density <math>B</math> by the cross-section area {{nowrap|<math>A</math>:}}
<math display=block>\Phi = \frac{\mu_0\, N\, i\, A}{\ell},</math>

When this is combined with the definition of inductance {{nowrap|<math>L = \frac{N\, \Phi}{i}</math>,}} it follows that the inductance of a solenoid is given by:
<math display=block>L = \frac{\mu_0\, N^2\, A}{\ell}.</math>

Therefore, for air-core coils, inductance is a function of coil geometry and number of turns, and is independent of current.