116 Whitehead — Magnetic Effect of Electric Displacement. 



The density of the displacement current i^ q= ; since 



47r at 



the E.M.F, is alternating we have : 



F = F„j sin a 



^ 'K ^ da. 



and q—~Ym cos a -^^ 



47r at 



also, ~Y = angular velocity = 27rN = tt . 133 

 at 



K -v/2.8800 2j-.133.10' . ^^o , 



•■• ^ = S • (2K+l)X-63 - 3X1U" '^"^ " ^° ^•^■^- '^I'^'^trostatic 

 units. 



K V2.88OO 27r.l33.10' 



^-S • (2K+l)x-63-(3XlOTXlO-'^'"' ^^P''"' 

 K 14-6 



= -T^ -^TT cos a 



2K+1 10' 



K 10-3 ^ . 



.*. = -vv — r — r^ amjDeres, enective, per unit cross section. 



Each of the coils for the magnetic field contained 1200 turns 

 of 'No. 18 B. & S. magnet wire ; H, the intensity of the 

 magnetic field at the center of these coils, as calculated with a 

 neglect of the influence of the ends, was 200 i, i being the 

 current in amperes; as measured by the electromotive force 

 induced in an exploring coil of known area and number of 

 turns, H was 166 z, (area of exploring coil 25^^°"^, 400 turns ; 

 observed E.M.F., with 2*1: amps, in coil, 33'5 volts, 133 

 cycles). The resistance of each coil was about 9 ohms, and 

 the calculated value of the coefficient of self-induction was 

 L = -109 henry ; at 114 volts, 133 cycles, each took 1*3 amperes 

 which corresponds to a value '104 for L. If 6 be the differ- 

 ence in phase between the E.M.F. and current, i. e., the augle 

 of Jag, we have : 



^ . 27rNL 6-28 X 133 X -104 ^^ . . ^,0^0' 



tan = -^ — = = 9-3, whence 6 = 83 52' 



Now consider the phase relations between the displacement 

 current and the alternating magnetic field from the sketch of 

 the connections. Since the difference in phase between the 

 primary and secondary E.M.F's of a transformer is approxi- 

 mately 180°, the E.M.F. on the electrodes having passed 

 through two transformations has returned to coincidence of 

 phase with the generator E.M.1\ and may be indicated by 

 sin a. The resulting displacement current has the phase cos a 

 as shown above, i. e., differs by 90° from the generator E.M.F. 

 The E.M.F. impressed on the coils lias been transformed 



