ELECTRIC OSCILLATIONS AND ELECTRIC WAVES. 271 



39. A 2O-mile transmission line consisting of two No. 8 B. & S. 

 wires 18 inches apart center to center and short-circuited at the 

 distant end is connected to a io,ooo-cycle alternator of which 

 the electromotive force is 500 volts effective. Find positions of 

 voltage nodes, and find maximum voltage between the line wires 

 at the voltage antinodes when the ultimate steady state of oscilla- 

 tion of the line is established, line resistance being neglected. 

 Also find positions of current nod es andfind maximum value 

 of current in the line at the current antinodes. Ans. Voltage 

 nodes at distances of o, 9.3 and 18.6 miles from short-circuited 

 end of line; maximum voltage at voltage antinodes 1,552 volts. 

 Current nodes at distances of 4.65 and 13.95 miles from short- 

 circuited end of line; maximum current at current antinodes 

 2.293 amperes. 



40. An electric field like that which is represented in Fig. 191 

 decreases in intensity at the space-rate of 100 volts-per-centi- 

 meter per centimeter of distance along the axis of reference. 

 (a) Find the electromotive force around a rectangle in the plane 

 of the paper in Fig. 191, the rectangle being 30 centimeters long 

 (parallel to AB, Fig. 191) and 20 centimeters wide, (b) Find 

 the rate at which the magnetic flux through this rectangle must 

 be changing in order to produce this electromotive force around 

 it. (c) Find the rate at which the magnetic field in Fig. 191 

 perpendicular to the paper is changing because of the tapering 

 of the electric field. Ans. (a) 60,000 volts; (b) 6 X io 12 max- 

 wells per second ; (c) i X io 10 gausses per second. 



41. Consider two line wires (ribbons) A A', BE', Fig. 41, 

 and imagine the current in these wires (ribbons) to be distributed 

 so that the current at any point p is represented by the ordinate 

 y of a straight line CC. The magnetic field between the ribbons 

 is a tapering field as described in connection with Fig. 193 on 

 page 250, the lines of force of the field being perpendicular to the 

 paper in Fig. 40 and directed away from the reader. The 

 intensity of the magnetic field in gausses at any point p is equal 



