# Electric potential

Make sure you review the lesson about electric potential energy which defined the concept using a single positive charge as shown below. Then, you can study this lesson. 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 of 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 potential energy of using four charges will be 4 times the electric potential energy of using just one charge.

Say for instance the electric potential energy of one charge was 5 joules. Then, the electric potential energy 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 potential energy as small as 0.0002 joule.

## Definition of electric potential

By definition, the electric potential is the electric potential energy per charge

or
electric potential energy / charge

Electric potential energy is measured in joules and charge is measured in coulombs.

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

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

The electric potential 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 potential energy is 2.40 × 10-16 J.

Electric potential =
electric PE / charge

=
2.40 × 10-16 / 1.20 × 10-17

= 2 ×
10-16 / 10-17

= 2 ×10-16 × 10+17

= 2 × 10+1

= 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 potential energy will then be 4.80 × 10-16 J.

Electric potential =
4.80 × 10-16 / 2.40 × 10-17

= 2 ×
10-16 / 10-17

= 2 ×10-16 × 10+17

= 2 × 10+1

= 2 × 10 = 20 J/C = 20 volts

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

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