345 



look towards this extremity'. Of course the sense of the rotation 

 changes on reversal of one of the currents. 



Hence the bar assumes the shape of a rightliand screw, when the 

 CLu-renls /, and I^ are in righthand cyclical order. Farther the angle 

 over which tiie bar is twisted, is proportional to the total nnmber 

 of windings of tlie solenoid, which falls on tiie length of the bar, 

 to the intensities of the cui'rents, and in inverse raUo to the square 

 of the radius. 



Above we found an expression for tlie work of the ponderoniotive 

 forces (lA on the increase of the torsion da. If the torsion amounts 

 to «, we can integrate this expression, through which we get: 



1 



We find tliis work back in the first place in the elastic energy 

 U of the bar. If into the expression for this ^ KR' oy, we introduce 

 the above found expression for «, we get for this : 



i-OC 



Tiie rest, wiiich is of the same amount as U, is converted into 

 kinetic energy, or when we make the motion take place infinitely 

 slowly by means of external couples, into externa! work. 



Let us now inquire into the increase of magnetic field energy. 

 For this purpose we make use of tiie expression : 



T= i <IS i S?d 3>, 



which can be easily derived from (1). 

 Here we introduce : 



rf, m 



We get then : 



A 7' =J d S C{Sp, d A -Iv + i?,, d A 55,/) = ^, m ff k I, I, R' 



Hence 



1 



^ + AT = iiufk IJJi'. 



4ü^ 



On the other hand on account of the torsion the quantity of 

 electricity 



