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55 



Effect of a Changing Magnetic Field. 469 



Calculation of the Effect. 



Let N = magnetic flux through the condenser. 



Q = quantity of charge, in electromagnetic units. 



C = capacity, 



E = charging E.M.F., 



F = electric intensity, 



y= force, in dynes. 



L — moment, in dyne-cm. 



n = frequency of alternation. 



6 = phase angle. 



Also let N, E, &c. indicate instantaneous values. 



A \ 



N, E „ „ maximum ,, 



N,E „ „ average 



N, E „ „ effective „ 



The instantaneous E.M.F. induced in a single turn of a 

 conductor encircling the magnetic field is dN/dt, and the 

 mean value at any instant of the electrostatic intensity around 

 a circle of radius r, is 



dt 2wr. 



The force exerted on the quantity AQ, distributed evenly 

 along an elementary annulus of radius r, is 



aV= ^N AQ. 

 7 dt '2ttv 

 The elementary moment is 



AT - * A Q 



and is independent of the radhis. Hence the total moment 

 exerted on any number of charged annuli of any width is 





Q 



2w 



- = r/N 



OE 



dt 



' 2tt 





Assuming both N and E to vary according to the sine law, 

 we have 



E = E sin 



N = N cos 9. 



