. I NDUCTANCE An electric current can be induced in a coil by flux change produced by another coil in its vicinity or flux change produced by the same coil. These two situations are described separately in the next two sub-sections. However, in both the cases, the flux through a coil is proportional to the current.
That is, Φ B α I . Further, if the geometry of the coil does not vary with time then, B I Φ ∝ For a closely wound coil of N turns, the same magnetic flux is linked with all the turns. When the flux Φ B through the coil changes, each turn contributes to the induced emf. Therefore, a term called flux linkage is used which is equal to N Φ B for a closely wound coil and in such a case N Φ B ∝ I The constant of proportionality, in this relation, is called inductance .
We shall see that inductance depends only on the geometry of the coil and intrinsic material properties. This aspect is akin to capacitance which for a parallel plate capacitor depends on the plate area and plate separation (geometry) and the dielectric constant K of the intervening medium (intrinsic material property). Inductance is a scalar quantity. It has the dimensions of [M L T – A – ] given by the dimensions of flux divided by the dimensions of current.
The SI unit of inductance is henry and is denoted by H. It is named in honour of Joseph Henry who discovered electromagnetic induction in USA, independently of Faraday in England. . .
Mutual inductance Consider Fig. . which shows two long co-axial solenoids each of length l . We denote the radius of the inner solenoid S by r and the number of turns per unit length by n .
The corresponding quantities for the outer solenoid S are r and n , respectively. Let N and N be the total number of turns of coils S and S , respectively. When a current I is set up through S , it in turn sets up a magnetic flux through S . Let us denote it by Φ .
The corresponding flux linkage with solenoid S is N M I Φ = ( . ) M is called the mutual inductance of solenoid S with respect to solenoid S . It is also referred to as the coefficient of mutual induction . For these simple co-axial solenoids it is possible to calculate M .
The magnetic field due to the current I in S is μ n I . The resulting flux linkage with coil S is, (