Question

Given the electrical potential energy, how do you calculate electric potential?

Answer 1

Here first we will discuss what is electrical potential energy and electric potential and what is the formula for potential energy and then derive the formula for electric potential.

Complete answer:
Electric potential energy is defined as the total potential energy a unit charge will possess if it is located at any point in outer space. The magnitude of electric potential energy depends on the amount of work done in moving an object from one point to another against the electric field. When the object is moved against the electric field it gains some amount of energy which is defined as the electric potential energy. Electric potential energy is a scalar quantity and possesses only magnitude and no direction. It is measured in terms of joule and denoted by $U$. SI unit of electric potential energy is $Joule$. The formula of electric potential energy is
${{U}_{E}}=k\dfrac{{{q}_{1}}{{q}_{2}}}{r}$
Where ${{U}_{E}}$ is the electric potential energy, $k$ is the coulomb constant, ${{q}_{1}},{{q}_{2}}$ are the charges and $r$ is the distance between the charges.

Now talking about electric potential, a charge placed in an electric field possesses potential energy and is measured by work done in moving the charge from infinity to that point against the electric field. Electric potential is denoted by $V$ and its SI units are volts.For any charge , the electric potential is obtained by dividing the electrical potential energy by the quantity of charge. So let us now divide electrical potential energy by a charge $q$,
$V=\dfrac{U}{q}$
$\Rightarrow V= k\dfrac{{{q}^{2}}}{qr}$...............(As we are talking about identical charges)
$\therefore V=k\dfrac{q}{r}$
Which is the formula of electric potential.

Note: The basic difference between electric potential energy and electric potential is that electric potential at a point in an electric field is the amount of work done to bring a point charge from infinity to that point, while electric potential energy is the energy that is needed to move a charge against the electric field.