**INDUCTANCE AND MAGNETIC ENERGY**

In Section 1.3, we introduced inductance, *L, *as an electric circuit element. Alternatively, we may relate inductance to magnetic circuit (or field) quantities. Thus, we redefine the *inductance *of an *N-turn *co il as the flux linkage, *ג* *, *per unit current:

(formula 5)

In (5), *Φ* is the flux through each of the turns (or, the mean flux per turn). The unit of inductance is the* henry *(H).

For a magnetic circuit having *n *distinct coils, we may define n2 inductances by

(Formula 6)

where *Np *is the number of turns in the *pth *coil and where *kpq, *the *coupling coefficient *between the *pth *and *qth *coils, is defined as the fraction of the flux produced by the *qth *coil that links the *pth *coil. For *p **≠* *q,*

*Lpq *is called the *mutual inductance *between coils *p *and *q; *for *p *= *q, Lpp *is the *self-inductance *of coil *p. *If the *n *coils carry currents i1, *i2,...... *..., *im *it may be shown that the energy stored in the inductances is given by

(Formula 7)

Further, it may be shown that the same energy may be expressed, in terms of magnetic field quantities B and **H, as**

** **

* *(Formula 8 )