122 Mr. G. F. C. Searle on the 



On the surface of the expanding sphere there will be a 

 surface flux of magnetic induction along lines of latitude. If 

 fjbh be the flux per unit length of a line of longitude, we may 

 deduce from the last equation that h=vKe. But it is more 

 instructive to obtain this result in another way. 



Take a fixed circle with its centre on the axis OX and its 

 plane perpendicular to the axis, and let the circle subtend 

 an angle 26 at (fig. 1), the distance of from the circle 

 being r. Then just before the expanding sphere reaches the 

 circle the electric force is given by (5), while just after the 

 sphere has passed over the circle, the electric force normal 

 to the sphere is given by (4). Hence, by § 3, the flux of 

 electric displacement through the circle suddenly changes by 

 the amount ^K.er sin 6. Thus, if p be the infinitesimal thick- 

 ness of the wave, the tee-integral of the /m<?-integral of H, 

 round the circle, taken for the tune p/v, is equal to Air times 

 the change of flux of displacement, or in symbols 



f*p'v 



lirr sin I H dt = ^Ker sin 6 . 4-7T. 

 Putting dz = vdt, we find that, if 



= pHtfr, (9) 



then h = vKe (10) 



When e is directed away from the pole X, as in fig. 1, the 

 directions of h and of u are connected in the same way as 

 the rotation and translation of a right-handed screw working 

 in a fixed nut. 



§ 5. So far the charge has been supposed to be impulsively 

 set in motion. If, however, it is originally in motion and is 

 impulsively brought to rest, it is only necessary to take (4) 

 as applying to the field outside the sphere and (5) as applying 

 to the field inside it. Thus the directions of e and It are 

 simply reversed, while their magnitudes remain unchanged. 



§ 6. When the charge g is finite, there is a finite flux of 

 displacement, viz. K<?/47r, in the infinitely thin surface of the 

 expanding spherical wave, and this implies an infinite value 

 for E and involves an infinite amount of energy. But, as we 

 shall see in § 7, if a charge Q is distributed over finite sur- 

 faces or throughout finite volumes according to any given law 

 of distribution, this difficulty disappears and the formula (7) 

 enables us to calculate the electric and magnetic forces in the 

 pulse due to the sudden starting or stopping of an electrified 

 system when the pulse has travelled out a great distance from 



