452 Prof. Maxwell and Mr. F. Jenkin on the Elementary 



into the strength of the current, the intensity of the magnetic 

 field, and the sine of the angle between the lines of force and 

 the direction of the current. This may be more concisely 

 expressed by saying that if a conductor carrying a current is 

 moved in a magnetic field, the work done on the conductor by 

 the electromagnetic forces is equal to the product of the strength 

 of the current into the number of lines of force which it cuts 

 during its motion. 



Hence we arrive at the following general law, for determining 

 the mechanical action on a closed conductor carrying a current 

 and placed in a magnetic field : — 



Draw the lines of magnetic force. Count the number which 

 pass through the circuit of the conductor, then any motion 

 which increases this number will be aided by the electromag- 

 netic forces, so that the work done during the motion will be 

 the product of the strength of the current and the number of 

 additional lines of force. 



For instance, let the lines of force be due to a single magnetic 

 pole of strength m. These are Arrrm in number, and are in this 

 case straight lines radiating equally in all directions from the 

 pole. Describe a sphere about the pole, and project the circuit 

 on its surface by lines drawn to the pole. The surface of the 

 area so described on the sphere will measure the solid angle sub- 

 tended by the circuit at the pole. Let this solid angle =a>, 

 then the number of lines passing through the closed surface 

 will be mco ; and if C be the strength of the current, the amount 

 of work done by bringing the magnet and circuit from an infi- 

 nite distance to their present position will be Cmco. This shows 

 that the magnetic potential of a closed circuit carrying a unit 

 current with respect to a unit magnetic pole placed at any 

 point is equal to the solid angle which the circuit subtends at 

 that point. 



By considering at what points the circuit subtends equal solid 

 angles, we may form an idea of the surfaces of equal potential. 

 They form a series of sheets, all intersecting each other in the 

 circuit itself, which forms the boundary of every sheet. The 

 number of sheets is 47rC, where C is the strength of the current. 

 The lines of magnetic force intersect these surfaces at right 

 angles, and therefore form a system of rings, encircling every 

 point of the circuit. When we have studied the general form 

 of the lines of force, we can form some idea of the electromag- 

 netic action of that current, after which the difficulties of nume- 

 rical calculation arise entirely from the imperfection of our 

 mathematical skill. 



24. General Law of the Mechanical Action between Electric 

 Currents and other Electric Currents or Magnets. — Draw the 



