With the assumptions that the earth has a uniform specific resistance, and that the stream-lines of current of commercial frequencies in it may be taken approximately as those determined with resistance only taken into account, it is shown that the EMF induced by a varying current in a straight transmission line with earth return, in a conductor one cm long parallel to the line at a point p distant y
0 cm from the line, may be expressed by
(e. m. u.)
x and z being the distances from the two ends of the line to the foot of the perpendicular from p to the line. x or z is to be taken negative when p is outside the line, in either direction. Integrating this, the total EMF induced in a parallel line is obtained. As a result of application of the formula, the self-inductance of a single-conductor straight transmission line with earth return is shown to be
(e. m. u)
where D is the length of the line, r is the radius of the conductor. Lastly, the potential difference on earth surface is expressed in terms of the electrostatic capacities of the electrodes.
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