Motion of an Electrified Sphere. 



Mi* 



59 



Table II. — Yalues of 



U ' 



»!• 



M^/U . 



n,. 



M^/LV 



o-i 



0-1339 



0-6 



09519 



02 



0-2710 



0-7 



1-2087 



03 



0-4153 



0-8 



1-5652 



0-4 



0-5715 



0-85 



1-8183 



0-5 



0-7465 



0-9 



2-1787 



Let P be the momentum in the pulse, so that 



(40) 



where VEH denotes the vector product of the electric and 

 magnetic forces and the integration extends throughout the 

 volume of the pulse. Then, since the momentum of the 

 electromagnetic field is changed from M x to M 2 + P by 

 the action of the force F 12 , 



M 2 -M 1 + P=f-IWfc. 



(41) 



When the change of velocity of the sphere is effected in 

 the reverse direction, both E and H in the pulse are simply 

 reversed in direction without change of magnitude, as appears 

 from (1) and (2), and hence P remains unchanged. Hence 

 we have 



Mi-Mo + P^JF^ft (42) 



Combining these equations with (35) and (36), and writing 



P=P 1 + P 2 , 



where P l is in the same direction as iij and P 2 in the same 

 direction as n 2 , we have 



u 2 (M 2 - Mi + Pi + P a ) = Wj - V\ + W 



u^Mx - M 2 + P x + P 2 ) = Wi - Wo + W. 



Working out the scalar products, we obtain 



P 1 cosa + P 2 = M 1 cosa-M 2 + (W 2 -W 1 + W)^ 1 = X 1 



Pi + P 2 cos a = Mo cos a- Mj + (Wi- W 2 + W)V =X 2 . 



