| FB |
 |
| I |
Re-arranging the previous equation, we get:
| L | = | N |
|
This makes it look like the self-inductance is determined by B and I, but it is actually determined by the geometry of the coil and the material inside the coil. This is similar to what we saw with a capacitor, where the equation:
Q = C DV makes it look like the capacitance is determined by the charge and potential difference, while it is actually set by the geometry of the capacitor and the material between the capacitor plates.
For the case of an empty solenoid, the magnetic field is given by:
B = monI
| Therefore | L | = |
|
= | moNnA |
For a solenoid with N turns, a length l, and a cross-sectional area with a radius R, this can be written:
| L | = |
|
If the solenoid has a solid core, the mo is replaced by the magnetic permeability mm. Remember that mm is several hundred to a few thousand times larger than mo for ferromagnetic material.