# Electric Potential due to a Uniform E-field

The case of a uniform electric field is very similar to the case of a constant gravity field near Earth's surface. The ideas you already have concerning gravitational potential energy apply directly to the situation with a uniform electric field.

For gravitational potential energy, we found that

U = m g h

and h is the height, the distance parallel to the gravity field g. Horizontal distance -- distances perpendicular to the gravity field g -- do not matter. Work is done by (or against) gravity only as the height changes. Moving an object horizontally does no work to gravity -- or no work is done by gravity when an object is moved horizontally.

In exactly the same manner, if we move a charge q from point A to point B in a region with a uniform electric field E, work is done along the direction that is parallel to the E-field E. No work is done as the charge moves perpendicular to E,

U = - F s

or

V = - E s

For a displacement s along the direction of the E-field E, then, this is just

V = E s

or

E = V / s

Notice that this means the units of E-field are V/m. Our earlier definition of E meant that E was mueasured in units of N/C. That is

V / m = N / C