Equivalent Shell of a Circular Current. 141 



Now, we know, the whole charge q passing any section of 

 i closed circuit as the magnetic induction threading it 



N 

 changes from zero to JN, is — „-. 



or 



47rm _ N 



k=-l. 



Also, as N due to pole m threading the circuit when the 

 semi-vertical angle subtended by the coil is 0, is given by 

 the relation 



AT , 27rO-cos#) 



JS =4:7rm . — — i — 



47T 



= 2irm . (1 — cos0), 

 we can easily see that, if Jc= — 1, the induced E.M.F. 



E = 27r?n . sin 6 .-=- 

 at 



_dN 



This shows Laplace's law may be taken to be true for the 

 44 magnetic current/' as much as for the electric current, 

 only the directions of the magnetic current and the electro- 

 motive force are related by a /^-handed cork-screw rule, 

 This would then give the expression for the electric induction 

 at points in the plane of the circular " magnetic current" in 

 a form similar to that for the magnetic induction due to an 

 electric current. We should get an Equivalent Dielectric 

 Shell, subject to the same conditions as the Equivalent 

 Magnetic Shell, satisfying the relation 



e = AKvm (iv.) 



and the Total Stress Energy in the I Electric Field would be 

 oiven by the relation 



r f r * 



KR 2 . _ _ . KmV 



x .ay .az= A 



6tt j a 



§ 5. Evaluation of A. 



From available tables the value of A to 81 terms has been 

 found by Messrs. Joshi and Sinha to be -914336179. The 

 series, however, is very slowly convergent and the sum to a 

 much higher number of terms is- necessary. 



