Electric Potential

Electrical Energy

Recall that a . We also know a joule is the same as a newton-meter. So we multiply force (from Coulomb's law) by radius to get .

Equation

The sign will come from how the charges interact.

Example

Determine the electric potential energy of two µ charges held apart. Also calculate the energy if one of the charges is negative.

solution

If one of the charges was negative:

Potential Energy Difference

From law of conservation of energy:

We know that , we can write:

Definition

Potential energy difference is the work required to bring a test charge from point to .

This brings us to the equation:

Equation

Electric Potential Difference

Electric potential difference is the potential energy difference per unit charge:

Equation

For a non-uniform field, we integrate to find:

Potential (Volt)

Also see SI Units#Volt (V), Voltage.

Question

What's the electrical potential energy around one charge?

Answer

Definition

Voltage is electric potential difference between two points. 1 volt is defined as bringing a test charge of from infinity to a point where of energy is consumed.

The volt is therefore the same as , and, .

Example

Determine the change in potential from away from a µ charge to away.

solution

Remark

If we do what the particles want, the change is negative. If going against, the change is positive.

So we see that the volt is nothing but electric potential difference from infinity to a point.

Equation

(see improper integral)

Potential Gradient

This allows us to re-define E-fields using the Gradient Vector:

Equation