144 Crook — Electromagnetic Alternating Currents. 



of the residual magnetism in the yoke come in to affect the 

 induction measurements. If the vahies of curve 1 are sub- 

 tracted from those of curve 2, the result is nearly a continua- 

 tion of the straight line which gives the effect at low current 

 densities. 



The similar curves on Diagrams lY and Y taken by the 

 second method, and at different frequencies, show that the 

 effects of the alternating current on the residual magnetism in 

 iron are different for different frequencies, that for the lower 

 frequency being the greater. 



Curves 3, Diagrams lY and Y, show that the total reducing 

 effect of the current is approximately proportional to the 

 strength of the current. 



Curve 3, Diagrams lY and Y, show the reducing effect of the 

 external circular magnetic field from a current flowing through 

 the central copper rod. Curve 4 shows the effect of passing a 

 current down the central rod and back on the iron. 



The force at a point in a metal tube due to a longitudinal 

 current in the tube is expressed by the formula 



F=z (r'— r ') 



in which F is the force, w the current density per unit area of 



the cross section, r the distance of the point from the axis of 



the tube, and r^ the inside diameter. From this it is seen that 



at the inner surface of the tube, where t~t^^ the force is zero, 



2^ 

 while at the outer surface, where r=r„, the force is — . The 



. ^^ . . 

 average force in the tube due to a current flowing longitudi- 



nally along it is proportional to — where /% is the mean radius 



of all points in the tube. 



The magnetic force at a point outside a linear conductor is 

 expressed by 



r 



where i is the total current and r is the distance of the point 



from the axis of the conductor. It is, therefore, evident that 



the average force in the iron due to a current flowing along its 



2^ 

 cylindrical axis is proportional to — . The magnetic force in 



the iron when the system was connected for taking curves 4, 

 Diagrams lY and Y, was therefore one-half what it was when it 

 was connected for curve 3, and if the reduction of the residual 

 magnetism was due to the circular magnetic flux alone, we 



