Conceptual Physics

conservative nature of the electrostatic force means that the potential energy depends

solely on the configuration, not on how it was arrived at.

We conclude this section with a review of the relationship of the signs of work and

potential energy, since they can be confusing. In terms of work done on the system,

separating two charges with opposite signs takes positive work (force in the direction

of displacement) and increases their potential energy. Pushing together two like

charges also takes positive work, and also increases their potential energy. Checking a

computationally based answer against some of your own physics intuition may help

make this clear. For instance, if you have to pull apart opposite charges, it should seem

that you are doing work on the system, increasing its energy, and in fact you are.

The proper treatment of signs is summarized in the table below.

It takes 5.0 J of work by the right-

hand wand to separate the

charges. What is the change in

potential energy?

ǻKE = 0

ǻPEe = W (work done on system)

W = 5.0 J

ǻPEe = 5.0 J

24.2 - Sample problem: electric potential energy

In this problem, work is done on the system consisting of the charged particle q and the uniform electric field E. The particle is stationary both

before and after it is moved.

Variables

What is the strategy?

1. Calculate the work done in moving the particle from its initial to its final position.


2. Since there is no change in kinetic energy, the change in potential energy equals the work done on the system. Using the given values,
   calculate this change.

Physics principles and equations

The work done to move the particle against the field is

W = Fǻx

The force required to move the particle against the field is

F = qE

Since the charged particle is stationary before and after it is moved by the external force, ǻKE = 0. This allows us to apply the equation

A particle with a charge of 0.15

coulombs is in a uniform electric field

of strength 52 N/C. An external force

pushes the charge 0.12 meters

directly against the field.

What is the change in electric

potential energy?

change in electric potential energy ǻPEe

work done to move particle W

change in particle’s kinetic energy ǻKE = 0 J

force moving particle F

charge of particle q = 0.15 C

strength of electric field E = 52 N/C

distance particle moves ǻx = 0.12 m

(^438) Copyright 2000-2007 Kinetic Books Co. Chapter 24