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I understand Electric Potential as follows (I "synthesized" the definition from different definitions I found online):

The sum of Electric Potential Energy for a matter particle with an electric charge, or of a deposit of such matter (like a capacitor).

Is electric potential just the sum or measure of Electric Potential Energy for a given unit of matter with electric change?

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The sum of Electric Potential Energy for a matter particle with an electric charge, or of a deposit of such matter (like a capacitor).

What is the source of your definition. Normally, electrical potential, or voltage, between two points is defined as the work per unit charge required to move the charge between two points. For a capacitor where the electric field $E$ between the plates is considered to be constant, the electrical potential, $V$ is

$$V=Ed$$

Where $d$ is the distance between the two plates. Electrical potential energy is the energy that a positive charge $Q$ acquires when moved from the negatively charged plate to the positively charged plate (or equivalently, when a negative charge is moved from the positively charged plate to the negatively charged plate) and is equal to $QV$ or for the capacitor $QEd$.

Is electric potential just the sum or measure of Electric Potential Energy for a given unit of matter with electric change?

They are related but they are not the same. Electrical potential $V$ is not the same thing as electrical potential energy. For a capacitor the electrical potential between the plates is $Ed$, and the electrical potential energy acquired by a charge moving from one plate to another against the direction of the electric field is $QEd$. Electrical potential is work (energy) per unit charge. Electrical potential energy is work (energy).

For gravity the analogy is the gravitational potential energy of a object of mass $m$ at a height $h$ near the surface of the earth has potential energy with respect to the surface of the earth of $mgh$. On the other hand, its gravitational potential (work per unit mass in this case) is $gh$.

Hope this helps.

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  • $\begingroup$ Is the work per unit charge means "the amount of work needed to move a particle with electric charge between two points in space? $\endgroup$ – user155243 May 28 '19 at 14:50
  • $\begingroup$ @JohnDoea Yes, for a particle with charge $Q$ in coulombs the electrical potential is the work to required per unit charge (per coulomb) to move the particle between two points in an electric field. The two points don't necessarily have to be in space. They could, for example, be between the terminals of a resistor. The movement of charge could be against the force of the field (in which case the work increases the electrical potential of the charge) or in the same direction as the force of the field (in which case the charge loses potential. This is the case for a resistor). $\endgroup$ – Bob D May 28 '19 at 15:18
  • $\begingroup$ @JohnDoea It is defined as the negative of work done by the internal electrical forces on the test charge per unit test charge. $\endgroup$ – Shreyansh Pathak Jun 1 '19 at 17:53

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