The forces between electrical charges have an electrical potential energy associated with this force. The total ME = KE + gravitational PE + elastic PE + electric PE.

If a positive charge is moved in a uniform electric field in the same direction as the field, there is a change (decrease) in the electric potential energy of that charge. ΔPE electric = -qEΔd

It is the difference in potential that is important. If we set the initial d to be zero, then: PE electric = -qEd This is only true for a uniform field.

“d” is the magnitude of displacement in the direction of the electric field. Perpendicular motion does not change the PE.

If there are two charges, another equation is needed. PE electric = kq 1 q 2 /r The reference point is infinity. The ΔPEelectric is + for like charges and - for unlike charges.

What is the electric potential energy between two electrons that are two meters apart?

The electrical potential energy associated with an electron and proton is x J. What is the distance between these two charges?

PE electric depends on the charge. A more practical concept is electric potential: PE electric /q = V.

Electric potential is independent of charge. The reference point for electric potential is arbitrary, only the difference in potential is important. Therefore: ΔV = ΔPE electric /q The unit is the volt, which is equal to one joule per coulomb.

As a one coulomb charge moves through a potential difference of one volt it gains (or loses) one joule of energy.

Remember: PE electric = -qEd and ΔV = ΔPE electric /q. So: ΔV = Δ(-qEd/q) or ΔV = -ΔEd

Voltage difference between a point at infinity and a point near a point charge: ΔV = kq/r

These potentials are scalars, not vectors; there is no direction involved.

A 5.0  C point charge is at the origin, and a point charge of -2.0  C is on the x-axis at (3.0m,0.0m). Find the total potential difference resulting from these charges between a point with coordinates (0.0m, 4.0m) and a point infinitely far away.

A battery does work to move a charge. As a charge moves through a 12V battery its potential is raised by 12V. If it is a 1 coulomb charge its energy is raised by 12 joules.