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Electric Potential Energy in a Uniform Force Field

Consider the +ve charge in the uniform electric field in the following diagram. This charge will contain an electric potential energy analogous to the way a mass would have a gravitational potential energy in a uniform gravitational field. (DEp=mgDh)

A force on the positive charge in the electric field, with a direction shown, would have a magnitude Eq, where E is the electric field strength and q is the magnitude of the charge.

F = Eq

The electric force on the charge has the potential to do work on that charge in moving from B to A which is equal to the difference in electric potential energy between point B and point A.Work is equal to force x distance so it follows that

W=DEEP=Eqd

compare with the equation for potential energy in a uniform gravitational field

DEP=mgDh

Note:
E	compares with	g
q	compares with	m
d	compares with	Dh

Symbol	Description	Units
W=DEEP	work or the change in electrical potential energy	J
E	the electric field strength	N/C
d	distance	m
q	Electric charge	C

Note: both gravitational fields and electric fields create conservative forces. Like potential energy where only the vertical height is considered (as opposed to the path) the electrical potential energy difference depends only on the start and ending positions. If a charge moves at an angle to the Electric field, only the component of the displacement in the direction of the electric field is considered.
There is a fair amount of confusion about the sign convention of electrical potential energy. Part of this confusion is caused because unlike gravitational fields where the force is always in the direction of the field, in electric fields the force may be in either direction depending on the type of charge. (+ve or -ve) Imagine the confusion this would bring for defining the location of the potential energy for a point charge. For gravitational fields we defined this at infinity because we knew that the energy at infinity is maximum. Is this so for electric charges? For a more simple example consider the diagram at the top of this page. The electrical potential energy is highest at the top of the diagram as shown but if the charge was negative then the electrical potential energy would be highest at the bottom of the page. Partly for this reason we often don't consider the electric potential energy but rather the electrical potential covered in the next lesson.

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