# What is the relation between ‘Electric Potential’ and ‘Electric Potential Energy’?

What is the relation between ‘Electric Potential’ and ‘Electric Potential Energy’?

• -1: this really shows no prior research effort. Mar 21, 2018 at 10:55

What is Electric Potential?

Electric potential (V) is the property of points in space. Electric potential can be defined in several ways:

1. The value of the electric potential at a point in space numerically gives the amount of work that needs to be done to bring a unit positive charge from infinity to that point.

2. A charge $q$ is said to have a potential energy of $Vq$ if it is at a point in space which has a potential of $V$.

For example, if you place a charge $q$ at a point, space nearby will have a non-zero value of potential. The electric potential at a point due to a charge at a distance $r$ from it is given by:

$$V = \frac{kq}{r}$$

What is Electric Potential Energy?

Electric potential energy (U) is the property of a system. Two charges in the vicinity of each other are said to have potential energy.

The electric potential energy associated with two charges separated by a distance $r$ is given by: $$U = \frac{kq_1q_2}{r}$$

• In 1. it isn't always infinity that's the reference point, though it often is with point charges. Electric potential is the amount of work it takes to move a unit positive charge from some reference point to the specified point. Jun 20, 2017 at 22:38
• Electric potential energy $U_e$ is the potential energy stored when charges are out of equilibrium (like gravitational potential energy).

• Electric potential is the same, but per charge, $\frac{U_e}q$. (Useful when comparing different points.)

• An electric potential difference between two points is called voltage, $V=\frac{U_{e2} }q-\frac{U_{e1}} q$.

• Regarding the third element of the list, voltage is the difference of the electric potentials of the two points only in electrostatics, right? If there're time-varying fields, then voltage is not the electric potential difference, because the work done (a line integral) is path-dependent, right? Jan 5, 2021 at 10:15

Yes there is! First, electric potential is measured in volts ($V$) and electric potential energy is measured in joules ($J$). Now if it sounds familiar is that both tell you about an energy quantity $V=\frac{J}{C}$. Indeed, in electromagnetism, the potential is seen as the electric field, multiplied by the distance between the source (for example a point charge) and the point on which you want to calculate the potential in volts.

• Yes, potentials in general can be calculated from the line-integral of a vector-field. No need to visualize an infinitesimal test-charge. The pattern of electric Potentials appears as space-filling surfaces, oriented 90deg to the e-field flux. If "lines of force" look like wads of infinitely-thin hair, then voltage looks like stacks of infinitely-thin paper. Each point-charge carries a puff of radial field-lines, but also exhibits a matrioshka of nested spherical equipotential surfaces. Sep 14 at 23:39

The electric potential, $$\Delta V$$ is equal to the change in electric potential energy, $$\Delta U$$ per unit charge, so

$$\Delta U= q\,\Delta V$$

where $$q$$ is the charge and for an electron $$q=-e$$