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XXXIII. Note on the Electromotive Force in 

 Moving Conductors. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



1 SHOULD like to be allowed to call the attention of those 

 interested in the theory of electrodynamics to the method 

 of estimating the E.M.F. in moving conductors generally 

 employed by writers on this subject. The notation I use 

 will require no explanation, as it is universally adopted. 



In a closed circuit at rest it is known that the E.M.F. is 

 proportional to the time-variation of the flux of magnetic 

 induction through the circuit, i. e. across any surface bounded 

 by the closed circuit, and therefore that it is equal to 



C(dFdx dGdy dRdzl 

 J \ dt ds dt ds dt ds ) 



taken round the circuit. 



"We cannot of course determine from this result with abso- 

 lute certainty the E.M.F. in an unclosed circuit, or in each 

 element of a closed circuit ; but we know that our results will 

 be consistent with the foregoing if we assume the x component 

 in each conducting element at rest in a magnetic field to be 

 _dF_dyjr 

 dt da; 

 and similarly for y and z. 



If therefore the element were moving in a constant field at 

 rest, the reasonable assumption would appear to be that the 

 E.M.F. is 



_dF_d±. 

 dt dx ' 

 •7F 

 where the —=- in this case is the time-variation of F at the 

 dt 



onducting element assumed at rest while the field, otherwise 

 unaltered, moved, as a whole, with the reversed motion of the 

 conductor, the relative motion of field and conducting element 

 being the same, and i|r (whatever its meaning) being the 

 same as before ; because all our knowledge of motion can 

 only be relative, and it is impossible to say whether the con- 

 ductor or field is at absolute rest. 



Instead of this, however, it is generally assumed that the x 

 component of E.M.F. is in this case (moving conductor in 

 constant field) 



dt dt dx 



