From the Electromagnetic induction
139. Inductance
Let's study in detail what properties of a conductor determine the EMF self-induction that occurs in it.
Magnetic induction \(\overrightarrow{B}\), created by a current, is proportional in all cases to the current force. As magnetic flux \(\Phi\) is proportional to \(B\), then
\( \Phi \,\sim \,B \,\sim \,I \)
It can therefore be argued that
\( \Phi \,= \,L\,I \) (12-5)
where \(L\) is the coefficient of proportionality between the current in the conductive loop, and the magnetic flux created by it, penetrating this loop. The value of \(L\) is called the circuit inductance or the self-induction coefficient of the circuit.
Using the electromagnetic induction law and expression \((12-5)\), we obtain equality
\( \Large{\varepsilon}\small{_i} \,= \,\frac{\Delta{\Phi}}{\Delta{t}} \,= \,L\frac{\Delta{I}}{\Delta{t}} \) (12-6)
if we assume that the shape of the circuit remains unchanged and the magnetic flux changes only due to the change in current force.
From equation \((12-6)\), it follows that inductance is a physical quantity numerically equal to the EMF self-induction that occurs in a loop when the current force changes by one ampere \(1A\) per \(1 \,second\).
The inductance, like capacitance, depends on the geometry of the conductor: it depends on its size and shape but does not directly depend on the current force in the conductor. However, apart from the geometry of the conductor, inductance depends on the magnetic properties of the medium in which the conductor is placed. If the magnetic permeability \(\mu\) depends on the magnitude of the magnetic field, and, consequently, on the current force generating this field, then \(L\), too, will indirectly depend on \(I\) through \(\mu\).
The unit of inductance in the system of SI units is called henry \((H)\). The inductance of a conductor is equal to one henry, if the EMF self-induction in \(1V\) occurs in conductor when the current force changes by \(1A\) per \(1s\).