484 PARTICULAR CASES. 



500. EXAMPLES. For a sphere surrounded by parallel and 

 equidistant currents, the value of the strength of the field < produced 



o 



by the currents (497) is - irn-J.. 



The intensity of magnetisation is then (385) 



3/*- I ^_^-% I 

 -?ji, 



and the induction 



, T 



4>= -- *,!, 



^ ] 



If the sphere is placed in a cylindrical coil which is so long that 

 the effect of the ends may be neglected, it will also acquire a uniform 

 magnetisation. 



This would also be the case with an ellipsoid, and also with a 

 sufficient approximation for a cylinder, the axis of which would 

 coincide with that of the coil. 



501. In the case of a cylindrical coil of great length (495), the 

 strength of the field in the interior is 47^! ; the value of the intensity 

 of magnetisation of a long cylinder parallel to the field would be 

 k$ (292) or 47rvfc# 1 I, and the internal induction F l will be 47n<, or 



I 6w 2 # 1 I. 



If S is the section of the bar, the flow of magnetic induction 

 across it is 



F 1 S = 1 67^18, 



and the total flow, including in it the induction 471-^18 of the current, 

 has the value 



Q = 471-;^ (i + 47r/) IS. 



This value can be experimentally investigated, and we might deduce 

 from it the coefficient of magnetisation k. 



502. The determination of this coefficient is still more accurate 

 by means of a piece of soft iron in the form of a torus, which is 

 surrounded by equidistant currents (496). In this case the 



1 

 strength of the field produced by the currents is - - at each 



