Question

What are the units of electric potential energy, of electric potential, and of electric field?

Short answer

The unit of potential energy is $\mathrm{Joule}\left(\mathrm{J}\right)$, the unit potential difference is $\mathrm{volt}\left(\mathrm{v}\right)$, and the unit of electric field is $\frac{v}{m}$.

Step-by-step solution

Concept/Significance of

A unit of measurement is a precise magnitude of a quantity that is specified and recognised by convention or legislation and is used as a standard for measuring similar quantities.

Determination of the units of electric potential energy, of electric potential, and of electric field

The potential energy of two charges is given by,

$U=\frac{K{q}_1{q}_2}{r}$

Here, K is the coulomb constant,$q_1$,$q_2$are the charges in coulomb and r is the distance between charges in metre.

The unit of potential energy is given by,

$$\begin{gathered} \mathrm{U}=\frac{{\mathrm{C}}^2}{\mathrm{m}} \\ =\mathrm{Joule}\left(\mathrm{J}\right) \end{gathered}$$

The electric potential is the amount of potential energy per unit charge which is given by,

$v=\frac{U}{q}$

So, the unit of potential is given by,

$$\begin{gathered} \mathrm{V}=\frac{\mathrm{J}}{\mathrm{C}} \\ =\mathrm{volt}\left(\mathrm{v}\right) \end{gathered}$$

The electric field at a point is describe as the multiple of potential difference per unit distance between two points that can be given by,

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

So, the unit of electric field is given by,

$\begin{array}{l}E=\frac{volt\left(v\right)}{m}\\ =\frac{v}{m}\end{array}$

Thus, the unit of potential energy is $\mathrm{Joule}\left(\mathrm{J}\right)$, the unit potential difference is $\mathrm{volt}\left(\mathrm{v}\right)$, and the unit of electric field is $\frac{v}{m}$.