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## Definition - What does Voltage Gradient mean?

A voltage gradient is a difference in electrical potential across a distance or space. Mathematically, the voltage gradient (F) can be described in one dimension between points A and B as the difference in the potential (p) at A and B divided by the length between points, x, between A and B:

F = (pB – pA) / (xB – xA) = Δp/Δx

The mathematics can be extended into two or three dimensions, depending on the type of voltage gradient being evaluated.

Voltage gradients are important for corrosion protection surveying techniques such as direct current voltage gradient (DCVG).

At the core, voltage gradients arise from the electrical potential of a material. Electrical potential is a property dependent on the distance between the two particles at hand. For example, the potential (V) of a point charge is described as:

V = Q / (4π * ε0 * r),

where ε0 is the permittivity of a vacuum, Q is the charge, and r is the distance

As the distance increases, the potential lowers. As such, a voltage gradient manifests across a distance. In more realistic scenarios, intermediate materials such as insulators dampen or otherwise alter the voltage gradient.

In the context of corrosion, voltage gradients are useful for surveying corrosion protection in submerged pipes. Because pipes installed under the Earth's surface will corrode over time, they are generally protected with cathodic protection or anti-corrosion coatings. Over time, if these protection methods fail at certain locations, the electric potential at those locations will change due to the change in the exposure of the underlying metal. These changes can be detected at a distance by monitoring the voltage gradient above the pipe, as in DCVG surveying. Detection of voltage gradients leads to identifying areas of piping prone to corrosion damage and potentially preventing costly damage that could occur in the future.