The standard inductance formula is:
v = L * Δi / Δt
This represents that the voltage created is equal to a constant (L) multiplied by the time (t) rate of change in the current (i).
In other words, inductance creates voltage through a ratio of current change. This gets described in inductance units of H.
Self-inductance uses the above equation and is obviously easier to calculate than mutual-inductance as there are fewer variables.
Remember that inductance takes place from wire to wire and coil to coil but can't be measured independently in each stage.
The magnetic flux created cannot be parsed so a whole circuit must be measured.
This is why sub equations created by James Clerk Maxwell exist to parse out each portion of the total circuit to understand how much inductance was created by each part.
Using an inductance converter is a good way to make sense of the differences in micro and macro inductance.
Inductance Across A Wire
Working with an example of a straight wire we can calculate the inductance across the wire.
To do this we understand that Ldc (where DC illustrates nanohenries) is equal to the length (l) of the wire multiplied by the radius (r) of the wire (to give us the total area of the circuit).
Ldc = 2l * [ln (2l/r) - 0.75]
Mutual inductance becomes more complicated from the addition of the second set of wires and/or cores.
For this, you have to calculate the area of both parts of the circuit as well as the interaction between.
Lm,n = µ0/4π ∮ cm ∮ cn dxm · dxn / |xm - xn|
This double integral inductance formula known as the Neumann formula takes into account the total curves of the wires (cm and cn) and also the permeability of the space (µ0).
This gets further defined by the position of the wires (xm, xn) and their increments (dxm, dxn).