Chapter 18 – Part I -Potential

Things to remember Definition of WORK W=F d cos(  ) Definition of Potential Energy Work necessary to bring an object from some reference level to the final position. For the diagram PE=Mgh M

Picture a Region of space Where there is an Electric Field Imagine there is a particle of charge q at some location. Imagine that the particle must be moved to another spot within the field. Work must be done in order to accomplish this.

What (or who) must do this work? A. An external agent (person) B. The Field itself C. Either of the above D. Dr. Bindell

What we will do …. For the moment, assume the charge has MASS. (It may not.) Assume the charge is initially stationary. The charge is to be moved to the left. The charge is to be moved at CONSTANT velocity. + charge E Mr. ExternalMrs. Fields

During this process, who is pushing? A. Mr. External B. Mrs. Fields C. Dr. Bindell + charge E Mr. ExternalMrs. Fields

When we start the process, the charge that is stationary must be brought up to speed. A. This is work and must be accounted for. B. This is work but we don’t have to worry about it. C. Only Dr. Bindell worries about stupid stuff like this!

About the work that they do.. A. Mrs. Fields does more work than Mr. External. B. Mr. External does more work than Mrs. Fields. C. Both do the same amount of work. D. Each does the negative amount of work than the other does.

Start and Sop ENERGY is required to bring the charge up to speed (if it has mass). ENERGY is required to bring the particle back to rest (if it has mass). The sum of these two is ZERO.

So, when we move a charge in an Electric Field.. Move the charge at constant velocity so it is in mechanical equilibrium all the time. Ignore the acceleration at the beginning because you have to do the same amount of negative work to stop it when you get there.

Summary-- When an object is moved from one point to another in an Electric Field, It takes energy (work) to move it. This work can be done by an external force (you). FIELD negative You can also think of this as the FIELD doing the negative of this amount of work on the particle.

And also remember: The net work done by a conservative (field) force on a particle moving around a closed path is ZERO! Huh? What does this mean??

A nice landscape  mg h Work done by external force = mgh How much work here by gravitational field?

The gravitational case: 

Someone else’s path 

IMPORTANT (For a conservative field) The work necessary for an external agent to move a charge from an initial point to a final point is INDEPENDENT OF THE PATH CHOSEN!

The Electric Field Is a conservative field. No frictional losses, etc. Is created by charges. When one (external agent) moves a test charge from one point in a field to another, the external agent must do work. This work is equal to the increase in potential energy of the charge. It is also the NEGATIVE of the work done BY THE FIELD in moving the charge from the same points.

A few things to remember… A conservative force is NOT a Republican. An External Agent is NOT 007.

Definition – Potential Energy PE or U is the work done by an external agent in moving a charge from a REFERENCE POSITION to a different position. A Reference ZERO is placed at the most convenient position Like the ground level in many gravitational potential energy problems.

Example: E Zero Level q F d Work by External Agent W external = F  d = qEd= U Work done by the Field is: W field = -qEd = -W external

A uniform electric field of magnitude 290 V/m is directed in the positive x direction. A µC charge moves from the origin to the point (x, y) = (20.0 cm, 50.0 cm).(a) What is the change in the potential energy of the charge field system? [ ] J

Think about YOU being the external agent and you are therefore doing the work. YOU

Parallel Sheets of Charge

Parallel Sheets of Charge II

+ + Get to Work q q’

IMPORTANT RESULT The potential energy U of a system consisting of two charges q and q’ separated by a distance r Is given by: This also applies to multiple charges.

What is the Potential Energy of q’? Unit is JOULES

AN IMPORTANT DEFINITION Just as the ELECTRIC FIELD was defined as the FORCE per UNIT CHARGE: We define ELECTRICAL POTENTIAL as the POTENTIAL ENERGY PER UNIT CHARGE: VECTOR SCALAR

UNITS OF POTENTIAL

Furthermore… If we move a particle through a potential difference of  V, the work from an external “person” necessary to do this is q  V

Example Electric Field = 2 N/C 1  C d= 100 meters

One Step More

Consider Two Plates OOPS!

The difference in potential between the accelerating plates in the electron gun of a TV picture tube is about V. If the distance between these plates is 1.50 cm, what is the magnitude of the uniform electric field in this region?

Important We defined an absolute level of potential. To do this, we needed to define a REFERENCE or ZERO level for potential. For a uniform field, it didn’t matter where we placed the reference. For POINT CHARGES, we will see shortly that we must place the level at infinity or the math gets very messy!

An Equipotential Surface is defined as a surface on which the potential is constant. It takes NO work to move a charged particle between two points at the same potential. The locus of all possible points that require NO WORK to move the charge to is actually a surface.

Example: A Set of Equipotenital Surfaces