ANNULAR COIL. 113 



754. ANNULAR COIL. We have seen that in the interior of an 

 annular coil (496) the flow of force across an element ^S of the 

 section, at a distance x from the axis, is equal for unit current to 



The mean action on a surface S is then 



2H 



If the surface S is a circle of radius a, the centre of which is 

 at a distance R from the axis of the coil, we have 



and accordingly, 



Let us suppose that the section S is an ellipse, one* of the axes 

 of which, 2a, is perpendicular, and the other, 2^, parallel to the axis 

 of the ring; we have 



The mean action is the same as that for a circle of radius a ; it 

 is independent of the radius b. 



In like manner we shall have for a rectangle, one of the sides 

 of which, 20, is perpendicular, and the other, 2b t parallel to the axis 

 of the ring, 



x 



ft R+a 2*1 i a 1 la* 



= / 'R^ = R"L I + 3R i + 5R 1 + 



The mean action is still independent of the dimension ; the 

 same would be the case for any figure having an axis of symmetry 

 parallel to the axis of the ring. 



VOL. II. I 



