Equivalent Shell of a Circular Current. 137 



As H is constant when r is constant, 



] BdS=/i£lIdS=!L f H . 2wr . dr 



/1.3\ 2 5 /1.3.5V 7 , . 1 ... 



[For the supplementary equipotential surface extending 

 from the rim to infinity 



V=2™{|^P 1 (<?) + &c,+ ^Sr vl"«P-«W + &e.} 



= 0.as 0=*"; 



H = 2ir« 



and 



/1\ 2 2a 2 ^ /l . 3 V 4a 4 , /l . 3 . 5 V Ga" , . ~1 



Jl^P = ,£ H . 2^r . * = 4,r >i { \ + ( ^ . § 



/1.3V 5 , / 1.3.5 \» 7 , . ■ ■) 



This is numerically identical with (i.), the difference in 

 sign being due to the south face of the equivalent shell being- 

 turned towards the normal instead of the north face.] 



In (i.) the radius of the coil is involved. If, however, 

 we think of the current as being constituted by a total 

 electric charge e moving round the coil with a linear velo- 

 city v, 



v 



; — •£■ 

 \ua ' 



/1.3V 5 /1.3.5\ 2 7 , . ) 



■which is independent of a. 



