# Electric potential

Before you study this lesson about electric potential (EP), make sure you understand the lesson about electric PE

PE stands for potential energy. To avoid using potential energy too many times, we will PE from time to time.

Furthermore, we will use EP to refer to electric potential.

Make sure you don't confuse EP with electric PE!

In the lesson about electric PE, we defined electric PE using a single positive charge as shown below. There is nothing special about using one charge. We could in fact use two, three, or as many charges as we want. If we use four positive charges instead one, the magnitude of four charges is higher than that of one. This makes sense since you will have to do more work to move these four charges closer to the charged rod.

As a result, the electric PE of using four charges will be 4 times the electric PE of using just one charge.

Say for instance the electric PE of one charge was 5 joules. Then, the electric PE of using two of such a charge will be 10 joules.

Be careful! 1 charge does not mean 1 joule of energy. A charge could in fact generate an electric PE as small as 0.0002 joule.

### Definition of electric potential

By definition, the EP is the electric PE per charge

or
electric PE / charge

Electric PE is measured in joules and charge is measured in coulombs

The unit of EP is J/C or volts. It is also called voltage.

1 volt = 1 joule of energy per 1 coulomb of charge

The EP will thus have the same value at any point in an electric field.

Here an example to illustrate this. Say for instance we place a positive charge in an electric field.
Suppose the charge of the particle is 1.20 × 10-17 C and the electric PE is 2.40 × 10-16 J.

EP =
electric PE / charge

EP =
2.40 × 10-16 / 1.20 × 10-17

EP = 2 ×
10-16 / 10-17

EP = 2 ×10-16 × 10+17

EP = 2 × 10+1

EP = 2 × 10 = 20 J/C = 20 volts

Suppose we replace the particle that has a charge of 1.20 × 10-17 with one that has twice as much positive charge.

The charge of the new particle is 2.40 × 10-17 C and the electric PE will then be 4.80 × 10-16 J.

EP =
4.80 × 10-16 / 2.40 × 10-17

EP = 2 ×
10-16 / 10-17

EP = 2 ×10-16 × 10+17

EP = 2 × 10+1

EP = 2 × 10 = 20 J/C = 20 volts

Why did we have to establish a difference between EP (electric potential ) and electric PE? In electricity, we prefer to work with the electric PE per charge rather than dealing with the total electric PE.

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