The resultant magnetic force at every point of such a surface is in the direction of the normal (n) to the surface; every line of force therefore cuts the equipotential surfaces at right angles.
Bearing this in mind, one can readily imagine how close together the equipotential surfaces must lie near the summit of a high sharp mountain peak.
The presence, however, of apparatus or observers upsets the conditions, while above uneven ground or near a tree or a building the equipotential surfaces cease to be horizontal.
Take any equipotential surface enclosing the whole of the electricity, and suppose this to become an actual sheet of metal connected to the earth.
The equipotential surfaces are two series of ovoids surrounding the two poles respectively, and separated by a plane at zero potential passing perpendicularly through the middle of the axis.
Let us assume the field divided up into tubes of electric force as already explained, and these cut normally by equipotential surfaces.
Above the level plain of absolutely smooth surface, devoid of houses or vegetation, the equipotential surfaces under normal conditions would be strictly horizontal, and if we could determine the potential at one metre above the ground we should have a definite measure of the potential gradient at the earth's surface.
Hence the equipotential surfaces cannot cut each other.
If the shape of the equipotential surfaces near it is influenced by trees, shrubs or grass, their influence will vary throughout the year.
This only means that the equipotential surfaces are crowded together, just as they are near the ridge of a house.