CK-12-Physics - Intermediate

http://www.ck12.org Chapter 16. Electric Potential

Electrical Potential Energy

In our gravitational analogy, the energy that a charge possesses at the plate with the higher potential is analogous
to the energy a mass possesses above the ground. Additionally, now that we have found a way to create a uniform
electric field, we have an analog to a uniform gravitational field.

If a positive charge+qis placed at the positive plate inFigure16.5, it will be repelled by the positive charges on
the plate and move toward the negative plate. (Think of+qas the objectmfalling toward the ground.)

FIGURE 16.5

A positive charge moving toward the negative plate

What is the force acting on the+qcharge? Recall that the Coulomb force on a charge placed in an electrostatic field
isF=qE. The work that the electric field does on the charge is equal to the negative change in the potential energy
of the charge, just as in the gravitational case. We can find an expression for the electric potential energy by finding
the work that is done on the charge. Recall thatW=F∆x. We write

Wf ield=F∆x= (qE)∆x=−∆PE→

qE(xf−xi) =−∆PE→

qExf−qExi=−∆PE

The expression for the electric potential energy is thus:PEelectrical=qEx.

Recall that the equation for the gravitational potential energy isPEgravitational=mgh.

We can compare the terms in the gravitational and electrical cases as follows:

m→q

g→E

h→x

Thus, we see that our prediction for the equation of electric potential energy stated in the introduction of the lesson,
was correct!