How do we define an electrostatic potential? My teacher tried to explain it through teaching us gravitational potentials, and I have presented what I came up with under '3.The attempt at a solution'. Please see below and thanks in advance for any help in clarifying whether my understanding seems to be correct, and more importantly, I do not fully understand the words I have underlined and made bold at the end, so if someone could explain it carefully, I would very much appreciate it.
Please see below.
The Attempt at a Solution
To understand electric potentials, it is useful to first understand gravitational potentials. Not gravitational potential energy (Egpe), but gravitational potentials (Vgrav):
Vgrav = Egpe/m
V1 = mg(h1)/m
V1 = g(h1)
(Egpe = mgh)
Do you see how gravitational potential (Vgrav) is a property of a point in space! There is no mass (m) in the equation Vgrav=gh!!!
Because of the gravitational field, we can define this property in a point in space known as the gravitational potential, and a mass in that field will gain gravitation potential energy due to the gravitational potential. Different masses will gain different amounts of gravitational potential energy, but the gravitational potential is a constant for any given uniform gravitational field:
Vgrav * m = Egpe
So, in an electrical circuit, the electrons gain electrostatic potential energy, but the electrostatic potential is defined as the electrostatic potential energy per unit charge. The electrostatic potential is a property of a point in the circuit, and a certain amount of charge will have some amount of electrostatic potential energy depending on where in a circuit it is.