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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