Section 3.3 · Worked examples · 2 of 2
Worked example 3.3.2: Earth electrode: touch and step voltage
About the worked examples of Section 3.3
The two worked examples below put numbers into the two applications. Each one uses only , and the three Laplace solutions of Problems 3.3.1–3.3.3, with no new physics. Numerical constants: , , , .
Earth electrode: touch and step voltage
#cf. Application 3.3.2
Given. A hemispherical earth electrode of radius , soil resistivity , fault current . Remote earth is at .
Find. (a) the earth potential rise and the electrode resistance , (b) the touch voltage for a person 1 m from the electrode, (c) the step voltage (1 m) at and , and (d) at .
The current leaves the electrode radially and crosses hemispheres of area , so and . No charge accumulates in the soil (), so obeys Laplace's equation, and the solution is the potential of Problem 3.3.3:
Hand on the electrode (), feet at , where :
Feet at and give , and feet at and give .
The estimate overestimates the step voltage, because falls as within the step. The exact value is .
Units: is in , and the touch voltage is smaller than the earth potential rise , as it must be, since the feet are not at remote earth.
Touching the electrode from 1 m away puts 21 kV across the body, while merely standing next to it, with the feet 1 m and 2 m from its centre, puts 8 kV between the feet. Both are largest where is largest, next to the electrode. The remedy is a flatter potential, provided by a buried equipotential mesh (Application 3.3.2).