274 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



is the velocity of progression of electric waves along the line. 

 Assume in this problem that the resistance of the bounding metal 

 sheets is negligible. 



Note. A wave of starting travels out from the battery end of the line at 

 velocity V. Ahead of this wave of starting the line is wholly undisturbed. Behind 

 this wave of starting the current in each line has everywhere the same value i (out- 

 wards in one line, backwards in the other line), the electromotive force between mains 

 is everywhere equal to 1,000 volts, the electric field intensity between the ribbons 

 has everywhere the same value, and the magnetic field between the ribbons has 

 everywhere the same value H. The electric energy per unit length of the pair of 

 ribbons may be calculated with the help of equations (65^) and (62) by considering 

 the ribbons as the two plates of a condenser, the electromotive force between them 

 being 1,000 volts. The intensity of the magnetic field between the ribbons may then 

 be found from the fact that the electric energy must be-equal to the magnetic energy, 

 and the current in each ribbon may then be found from the relationship established in 

 problem 147. Calculate the intensity of the electric field, the intensity of the mag- 

 netic field, and the current in each ribbon in the region behind the wave of starting 

 in problem 148. 



149. The end of the transmission line (pair of ribbons) in prob- 

 lem 148 is short-circuited by zero resistance. Make a diagram 

 showing the distribution of electric and magnetic field, the distri- 

 bution of charge on the two ribbons and the distribution of cur- 

 rent along the_two ribbons at an instant after the wave of starting 

 has been reflected from the short-circuited end of the line. 



Note. The student should read Art. 136 of Franklin and MacNutt's Elements 

 of Mechanics in order to be able to understand this problem. 



150. The end of the transmission line (pair of ribbons) in 

 problem 148 is open, that is the two ribbons come to an end in 

 air. Make a- diagram showing the distribution of electric and 

 magnetic field, the distribution of charge on the two ribbons and 

 the distribution of current along the two ribbons at an instant 

 after the wave of starting has been reflected from the open 

 end of the line. 



151. The transmission line specified in problems 148, 149 and 

 i 50 is assumed to have zero resistance, and the short-circuit at 

 the end of the line is assumed to have zero resistance in problem 

 149 so that the current produced by the battery in problem 149 

 ultimately becomes indefinitely large. Plot a curve showing the 

 growth of current at the battery terminals with lapse of time. 



