43 6 CURRENTS AND MAGNETIC SHELLS. 



The action of the lower pole P' is obviously null ; for any portion 

 of the flow of force starting from this point, and which meets the 

 sheet, necessarily cuts it twice, entering first by the positive, and 

 then by the negative face ; there cannot, therefore, be any variation 

 of energy on this side, and therefore no cause of motion. 



If the two poles were beyond the line AB, which joins the ends 

 of the movable current, the action of each will be null, and there 

 will be no rotation. In like manner, if the two poles were in the 

 interval AB, the total variation of the flow of force relative to any 

 displacement of the arc will be null, for the two poles will produce 

 equal and opposite variations. The arc must, therefore, be at rest. 



These various experiments are due to Faraday. 



457. ANOTHER FORM OF EXPRESSION FOR THE. ELECTRO- 

 MAGNETIC; WORK. In the preceding example the work 2mW 

 corresponding to a rotation is equal to the product of the 

 strength of the current by the flow of force cut by the arc ACB in 

 the displacement. It is easy to generalise the expression for the 

 work in this new form. 



Let us consider, in fact, a fixed magnetic system, in the field of 

 which a current experiences any given displacement or deformation. 

 Let s and s' be the two successive positions of the current (Fig 102), 



and Q and Q' the flows of force which traverse the negative face 

 in the two cases. The corresponding work of the electromagnetic 

 forces is I(Q' - Q). 



Draw two planes P and P' tangential to the two positions of the 

 circuit ; join the points of contact AA', and BB', and denote by Q x 

 and Q 2 the flow corresponding to the surfaces A'ACBB'C' and 

 A'ADBB'D'. We have evidently 



Q'-Q=Q 2 -Qr 



