CYLINDRICAL COIL. 479 



finite transversal dimensions ; it is approximately realised by winding 

 a wire in the form of a helix on the surface of the cylinder. Each 

 element of the helix may be replaced by its projections on the 

 axis and on a plane perpendicular to the axis. If the section of 

 the cylinder is small, we sensibly destroy the effect of the former by 

 bending the wire back in a contrary direction parallel to the axis. 



Whatever be the diameter, if the individual turns are sufficiently 

 near, and the coil consists of an equal number of layers in which the 

 inclination of the windings is alternately in opposite directions, the effect 

 of the projections on the axis is still sensibly zero, and the external 

 action differs very little from that of the perpendicular projections. 



The system of the currents perpendicular to the axis is equivalent 

 to a solenoidal magnet of the same form ; we may, in fact, replace 

 each of them by a shell, and decompose the system into an infinity 

 of parallel solenoids, each of which is equivalent to a solenoidal 

 filament. 



The action of the system on points outside the cylinder, reduces 

 then to that of two equal and opposite layers spread uniformly on 

 the bases, and the density cr of which is n-J.. 



For internal points the force is equal to the induction of the 

 equivalent magnetic system. If the cylinder is so long that the 

 action of the ends may be neglected in part of its extent, the lines of 

 force are parallel to the axis of the cylinder ; the field is uniform and 

 its strength is 



The flow of induction across the section of the cylinder is 



this flow is in the opposite direction to the internal flow from the 

 bases of the equivalent magnet. 



It is, moreover, evident that a coil is not equivalent to a hollow 

 magnet ; in the hollow magnet all the lines of force, both internal and 

 external, start from the positive surface, and are absorbed at the 

 negative surface ; in coils, on the contrary, the internal lines of force 

 are the continuation of the external lines of force, and form closed 

 curves which never terminate at magnetic masses. 



496. ANNULAR COIL. Suppose a ring to be covered by equal 

 currents equidistant from each other, and each situate in a plane 

 passing through the axis ; the system may be decomposed into a 

 series of solenoids, and it is equivalent to a solenoidal magnet of the 

 same form (411). 



