JVotes on Electricity and Magnetism. 429 



In the usual presentation of the rails and slider illustration 

 the sliding bar has length I between the rails, which are laid 

 in a magnetic field o£ uniform intensity H, so that the bar, 

 moving with speed v in a direction at right angles to its 

 length, cuts perpendicularly across the lines of force of the 

 impressed field. The rails are connected by a wire so that 

 the total resistance of the circuit is It ; and for simplicity 

 the rails and slider are regarded as being of negligible re- 

 sistance, so that R may be taken as practically all contained 

 in the wire. It is explicitly assumed (B. A. Rep. loc. cit.) 

 that the speed v of the slider and the current produced by 

 the motion are both constant. The following investigation 

 will show that this assumption is untenable. 



The applied electromotive force in the circuit is ~H.lv, due 

 we suppose to motion of the slider caused by an external 

 agent acting against the electromagnetic forces applied to 

 the bar ; and, if we suppose the self-inductance at a given 

 instant to be L, and the current 7 to be constant, the equa- 

 tion of motion is 



HZf>-i/y=R7, (1) 



since clearly as the slider moves L must vary. The condition 

 that 7 is constant gives also 



Hft=Ly (2) 



The rate at which work is done on the slider by an ex- 

 ternal agent is Hlvy, and this is spent in the rates JL7 2 , 

 at which the electrokinetic energy JL7 2 is increased, R7 2 at 

 which heat is produced in the circuit, and the rate mvv at 

 which the kinetic energy j^mv 2 of the sliding bar is added to. 

 Thus we obtain 



Hlvj=mvv +1L 7 2 + R7 2 (3) 



To make the equations quite general we might have in- 

 cluded the effect of a motor (or its equivalent in the form of 

 electrolytic cells, or the like) in the circuit. If E be the 

 back-electromotive force of such an arrangement, due to 

 the performance of work otherwise than in the direct pro- 

 duction of heat, equation (1) becomes 



Hfo-L7=E~+%; (4) 



and instead of (3) we have 



Hlvy=mvv + } i Ly 2 + Ry+\\y 2 , ■ - • (^ 



where R is the total resistance in circuit. 



Phil. Mag. 8. 6. Vol. 27. No. 159, March 1914. 2 a 



