INDUCTANCES AND RESISTANCES 



The magnetic circuit 



When a current / flows through a coil of insulated wire, a magnetic field is 

 set up which may be visualized as lines of force threading the coil, emerging 

 at one end, passing outside the coil to the other end, and re-entering there. 

 If the direction of current flow and the direction of the winding are as in 

 Figure 4.1, the lines of force outside the coil pass up the paper as shown, 

 and there is a north-seeking pole at the bottom of the coil, and a south- 

 seeking pole at the top. The strength of the magnetic field is proportional to 

 the current, to the number of turns, and to factors depending on the geometry 

 of the coil. The total number of fines of force, or flux, is 



</>air -4NI 

 where KyjK^ is the proportionality factor and A'^ is the number of turns. 



Flux path 



Figure 4.2 



More lines of force are brought into being if they are provided with a 

 path of low magnetic resistance or 'reluctance' to travel in. Thus if a closed 

 ring or 'core' of iron or iron compound be provided, nearly all the flux is 

 found to lie in the 'magnetic circuit' so produced, and to be proportional to 

 a factor called ^, the 'permeability' of the iron (often of the order of 100 or 

 1,000), and inversely proportional to the length of the magnetic circuit 

 {Figure 4.2) 



^ 



iron 



IxK^NI 

 IK, 



Magnetic Ohm's law — If we compare the equation above with that for an 

 elementary electrical circuit, / = {\jR)E, we see that if current is analogous 

 to flux, then E, the electromotive force, is analogous to K^NI, the 'magneto- 

 motive force', and 1//? is analogous to fijlK^- Thus, KJf [x corresponds to 

 R, and is the reluctance of the magnetic circuit. 



Air gap — It often happens that a magnetic circuit is provided with an 



54 



