EJ.ECTRIC INDUCTION. 



infinite plane sheet has been solved, taking into account the mutual induction 

 .f these currents, so as to make the solution applicable to a sheet of any degree 

 of conductivity. 



The statement in equation (10), that the motion of a magnetic system 

 does not produce differences of potential in the infinite sheet, may appear some- 

 what strange, since we know that currents may be collected by electrodes 

 touching the sheet at different points. These currents, however, depend entirely 

 on the inductive action on the part of the circuit not included in the sheet; 

 for if the whole circuit lies in the plane of the sheet, but is so arranged as not 

 to interfere with the uniform conductivity of the sheet, there will be no dif- 

 ference of potential in any part of the circuit. This is pointed out by Feliri, 

 who shews that when the currents are induced by the instantaneous magnetiza- 

 tion of a magnet, these currents are not accompanied with differences of potential 

 in different parts of the sheet. 



When the sheet is itself in motion, it appears, from Art. GOO of my treatise 

 On Electricity and Magnetism, that the electric potential of any point, as 

 measured by means of the electrodes of a fixed circuit, is 



ff f 



where -rr, '^, \\ are the components of the velocity of the part of the sheet 



i ' i ' Ot 



to which the electrode is applied. 



In the case of a sheet revolving with velocity t about the axis of z, tlii.s 

 becomes 



dP d 



Note 2. The velocity R for a copper plate of best quality 1 millimetre in 

 thickness is about 25 metres per second. Hence it is only for very small velo- 

 cities of the apparatus that we can obtain any approximation to the true result 

 by neglecting the mutual induction of the currents. Feb. 13. 



