272 ADVANCED ELECTRICITY AND MAGNETISM. 



to 4?r times the abamperes of current per centimeter of width 

 of ribbons. The current at the point pp is 50 amperes per unit 

 of width, and the current at point p'p' is zero. Find the rate 

 at which the electric field from ribbon A A' across to ribbon BB' 

 is increasing in volts per centimeter per second. 



A P tf A' 



Note. The simplest method of handling this problem is to calculate the rate 

 at which charge is accumulating on each square centimeter of the inner face of the 

 ribbons due to the tapering current, positive charge on ribbon AA' and negative 

 charge on ribbon BB', and to consider, with the help of Gauss's theorem, the inten- 

 sity of the electric field which is associated with these charges as follows. Consider 

 one square centimeter of the inner face of the upper ribbon. The current which 

 flows into this area across one side is one ampere greater than the current which 

 flows out of it on the other side according to the data of the problem, and therefore 

 one coulomb of charge is collecting per second upon each square centimeter of the 

 inner faces of the ribbons. The total electric flux which emanates from one 

 coulomb of charge is 1.131 Xio 13 lines, where one line is the amount of flux crossing 

 one square centimeter at right angles to an electric field of which the intensity is 

 one volt per centimeter. Therefore, since one coulomb of charge is collecting per 

 second on each square centimeter of the ribbon A A', it follows that the electric 

 field between the ribbons is increasing at the rate of 1.131 X io 13 volts per centi- 

 meter per second. 



42. A long wire of which the resistance per centimeter of 

 length is 0.02 ohm carries a current of 30 amperes, (a) Find the 

 rate at which energy flows in upon each centimeter of length of 

 the wire in ergs per second, (b) Find the intensity of the energy 



