The easiest way to determine an inductance is by using an RLC measuring bridge. Since this isn't a very cheap solution, most of the time the step response of an RL circuit is used in combination with an oscilloscope.
For more details have a look a this site:
How to Measure Inductance?
No, it isn't symmetric in that sense.
In a circuit that consists primarily of inductance and resistance, there's a time constant associated with its transient response1 that works out to
$$\tau = \frac{L}{R}$$
In the igntiion circuit, you basically have a battery, a switch and the ignition coil in series. \$R\$ represents the total resistance of all three. Two of them have constant resistance, but the switch varies between very low and very high resistance.
When the switch is closed, the total \$R\$ is low (dominated by the resistance of the battery and the coil), which means that \$\tau\$ is relatively large — the current changes more slowly. When the switch is open, the total \$R\$ is extremely large (dominated by the switch), so \$\tau\$ is very small and the current changes very rapidly.
Therefore, since the voltage is determined by
$$V(t) = L\frac{dI(t)}{dt}$$
when \$\frac{dI}{dt}\$ is large, so is the voltage.
1 The transient response is of the form
$$I(t) = I_{\infty}+(I_0 -I_{\infty})e^{-\frac{t}{\tau}}$$
At t = 0, I(t) = I0 and at t = ∞, I(t) = I∞.
Best Answer
This is the formula for a simple solenoid: -
Basically if you space the (same number of) turns out, the length dimension (l) increases and inductance reduces.
As for a transformer core, adding an air gap significantly reduces the inductance. You have to think about the first formula and imagine that the solenoid was wound on a piece of ferromagnetic material such as ferrite or steel laminations. The dominant material that affects the inductance is not the core material but the air gap from one pole end to the other - imagine it like putting a 1k resistor in series with a 1 ohm resistor - the 1k dominates and represents the air gap; the 1 ohm is the core material and is totally dominated by the air gap.
For a closed transformer core a different formula is used because the core has no gap (or a very small gap) and the core dominates. However, introducing a small gap does reduce the effective permeability of the core significantly.
Usually this is specified on core data sheets but there are formulas that can be used to work this out. Ultimately, as gap becomes much more significant, that formula becomes the one at the top of this answer.
For an ungapped toroid: -
You can see it bears strong similarities with the solenoid formula but "mu" is the permeability of the core material and not air (or vacuum).
Pretty toroid pictures stolen for here
This is a good explanation for inductance with an air gap.