792 



Mr. A. Ferguson on tlie Construction and 



distance x from the centre 0. We have at once 

 F -2f(i + I), 



c(c + SB) 



and 



Pi 



c(c—%) 



s/c-+(c— %y 



?2 



</# + (? + a)' 



Substituting, expanding the radicals, and neglecting ~-^ 

 and higher powers of #, we obtain 



showing that the field is uniform over a small area near the 



x 2 

 centre if ~- 2 is negligible. 



§ 6. It now becomes necessary to find the magnitude of the 

 magnetic force at a point P on a line drawn through 

 perpendicular to the plane of the coil. 



Fiff. 3. 



In fig. 3, ABOD is in the plane of the paper, OP 

 ( = x) is perpendicular to the plane of the paper, and is the 

 centre of the rectangle. 



The force F at P due to AD will be localised in the 

 horizontal plane ROP as shown in fig. 4. 



Also the total force due to AD and CB will, by symmetry, 

 be along OP. 



.-. force at P due to AD = F = % Sm 6 } ' 



