ENERGY OF MAGNETIC FIELD. 13 



of the current. Thus the work, W, expended in creating the 

 magnetic field is given by 



(5) 



Energy of the Magnetic Field. This is the energy 

 expended in driving the current against the counter E.M.F. of 

 self-induction from the instant at which the circuit is made to 

 the time when the current attains its maximum value, and it 

 has its equivalent in the potential energy stored up in the magnetic 

 field. 



CASE II. Field due to currents in two mutually induc- 

 tive circuits. 



If /i and /2 are the maxima values of the two currents in the 

 two circuits respectively, the energy expended in driving the 

 currents against their respective E.M.F.s of self-induction will 

 (by Case I.) be- 



\LJ? and iZ, 2 / 2 2 



where L\ and Z 2 are their respective coefficients of self-induction. 



There will, however, be opposing E.M.F.s in each circuit 

 due to mutual induction. If M be the coefficient of mutual in- 

 duction of the two circuits, and ii and i 2 be the instantaneous values 

 of their respective currents, the opposing E.M.F. in circuit 1 due 

 to mutual induction is ( 13) 



IT* 



M dt 



and that in circuit 2 is 



The rate at which work is being done against mutual induction 

 in the two circuits taken together is therefore 



and the whole energy expended in driving the currents against 



