68 ELECTRICAL ENGINEERING 



where n is the number of turns in the solenoid, 



A is the sectional area of the ring, 

 I is the mean length of the ring and 

 fj, is its permeability. 



When the current increases by a small amount di the flux in- 

 creases by an amount dcf> = - v , M di, and the work done is equal to 



the product of the current and the increase of the flux, 



. , 4:irn 2 A(jL . ,. 

 dco = m d<^> = - j - 1 di ergs. 



The work done while the current is building up to its full value 



w = 



where L = - | - is a constant and is called the inductance of 



the circuit. 



This amount of energy is stored in the magnetic field of the 

 solenoid and may be expressed in other forms. 



The energy stored is 



but the magnetic force in the solenoid is 



therefore, 



- 



or since the induction density is 



o$ 



the energy may be expressed as 



