mathematical derivation of potential difference
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Because it's derived from a force, it's a vector field. The electric potential is the electric potential energy of a test charge divided by its charge for every location in space. Electricity is a conservative force, so the work done by it doesn't depend on the path taken. This equation says something more astounding.
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The potential difference between points A and B, VB – VA, is defined to be the change in potential energy of a charge q moved from A to B, divided by the charge. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.
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