The Electric Potential

The electric potential is a scalar field: it labels each point in space with a value (but no direction). The value is related to the amount of energy it takes to move an electric charge to that point.
The gravitational potential energy between two objects depends on the difference in their positions with respect to the gravitational field (i.e. up or down from the ground). The electric potential energy between two objects depends on the difference in their positions relative to the electric field (i.e. toward or away from electric charges).
Electric potential energy can be exchanged for kinetic energy, or gravitational potential energy, or spring potential energy, etc.
If a charged object moves in an electric field from point A to point B, the change in its electric potential energy is equal to
```
            delta EPE  =  - (work done by electric field)                
```

The change in electric potential as a charged object moves from point A to point B is defined as

                             delta EPE
            delta V    =   ---------------
                           charge on object

The units of electric potential are (Joules / Coulombs) = Volts.
The electron volt is a unit of energy: it is the amount of energy an electron would gain if it moved through a potential difference of -1 Volts:
```
                1 eV =  [-1.602 x 10^(-19) C] * [-1 volts]

                     =  1.602 x 10^(-19) Joule
```

The potential difference between two points A and B due to a point charge q is

                           ke * q        ke * q
             V  - V     = ---------  -  ---------
              B    A          r             r
                               B             A

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Answer to Challenge Question
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