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### Electrostatics

The governing equations of electrostatics are

| (23)

and

| (24)

where is the electric field, is the electric potential and is the electric charge density. The electric field is the force on a unit charge. For metals, it is linked to the current density by the electric conductivity [5]:

| (25)

The resulting equation now reads

| (26)

Accordingly, by comparison with the heat equation, the correspondence in Table (5) arises. Notice that the electrostatics equation is a steady state equation, and there is no equivalent to the heat capacity term.

Table 5: Correspondence between the heat equation and the equation for electrostatics.
heat | electrostatics
T |

An application of electrostatics is the potential drop technique for crack propagation measurements: a predefined current is send through a specimen. Due to crack propagation the specimen section is reduced and its electric resistance increases. This leads to an increase of the electric potential across the specimen. A finite element calculation for the specimen can determine the relationship between the potential and the crack length. This calibration curve can be used to derived the actual crack length from potential measurements during the test.

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