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Home Logarithmicpotential Theory Computation of Potential Gradients  
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Computation of Potential GradientsAuthor: Edmund A. Laport
One is usually interested to know the gradient near the highpotential wires of a feeder when a power W is being transmitted into the feeder that is correctly terminated in its characteristic impedance. Then
Then, since the potential gradient [#nabla#]V = f( ρ) for a given configuration of wires, Then the approximate potential gradient [#nabla#]V will be
This is applied to practical design problems as follows: Assume that it is desired to find the approximate potential gradient at the surface of a cylindrical wire of radius 0.100 inch when its potential with respect to ground is 10,000 volts. The wire is far removed from all other wires so that its peripheralcharge distribution is uniform and its electric field strictly radial. We can employ the device of assuming that this wire is the inner conductor of a coaxial transmission line of very high characteristic impedance  say 400 ohms arbitrarily. For such a value the radius R of the outer conductor must be (from the characteristicimpedance formula for the coaxial line) and the ratio R/ ρ = 791.7. If now we increase ρ by 0.005 inch, so that we can compute the potential at a point 0.005 inch from the wire, and apply the equation previously derived for the potential at a point in the dielectric space of a coaxial line, we obtain, by using fiveplace logarithms,
The fall in potential across the first 0.005 inch from the wire is
The average gradient across this distance is then 73/0.005 = 14,600 volts per inch. The same method can be applied to determine the potential gradient at the surface of the highpotential wires of any transmission line for which the characteristicimpedance formula is known. The reason for this is that when the charge per unit length remains constant, the potential of a wire decreases as its periphery increases, or, as a consequence, as its characteristic impedance decreases. Since the accuracy of the results depends upon the accuracy of very small differences, sliderule accuracy is not sufficient and the computations should be carried out to four or, preferably, five significant decimal places.


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