Chapter 20

Copyright © 2010 Pearson Education, Inc.

Lecture Outline

Chapter 20

Physics, 4th Edition

James S. Walker


Chapter 20

Electric Potential and Electric Potential Energy


20-1 Electric Potential Energy and the Electric Potential

The electric force is conservative; therefore, there must be a potential energy associated with it.

It takes work to move an electric charge perpendicular to an electric field:

As usual, the change in potential energy is the negative of the work:



Just as it was useful to define the electric field, it is useful to define the electric potential (NOT potential energy):

The electron volt is a unit of energy:



The electric field is related to how fast the potential is changing:


20‐1 Electric Potential Energy and the Electric Potential








20-2 Energy ConservationIn general, for a mass moving from A to B due to a conservative force,

For the electric force,

so that


20-2 Energy Conservation

Since the force on a negative charge is opposite to the field direction,

Positive charges accelerate in the direction ofdecreasing electric potential;

Negative charges accelerate in the direction ofincreasing electric potential.

In both cases, the charge moves to a region of lower potential energy.


20‐2 Energy Conservation








20-3 The Electric Potential of Point Charges

The difference in potential energy between points A and B is



Therefore, the electric potential of a point charge is:

shown here for a positive and negative charge, respectively



The electric potential of a group of point charges is the algebraic sum of the potentials of each charge.


20‐3 The Electric Potential of Point Charges












20-4 Equipotential Surfaces and the Electric Field

On a contour map, the curves mark constant elevation; the steepest slope is perpendicular to the curves. The closer together the curves, the steeper the slope.



Electric potential and the electric field have the same relationship –there are lines (or, in three dimensions, surfaces) of constant potential. The electric field is perpendicular to these equipotential lines, and strongest where the lines are closest together.



For two point charges:



An ideal conductor is an equipotential surface. Therefore, if two conductors are at the same potential, the one that is more curved will have a larger electric field around it. This is also true for different parts of the same conductor.



There are electric fields inside the human body; the body is not a perfect conductor, so there are also potential differences.

An electrocardiograph plots the heart’s electrical activity:



An electroencephalograph measures the electrical activity of the brain:


20-5 Capacitors and Dielectrics

A capacitor is two conducting plates separated by a finite distance:


The capacitance relates the charge to the potential difference:




A simple type of capacitor is the parallel-plate capacitor. It consists of two plates of area Aseparated by a distance d.

By calculating the electric field created by the charges ±Q, we find that the capacitance of a parallel-plate capacitor is:



The general properties of a parallel-plate capacitor – that the capacitance increases as the plates become larger and decreases as the separation increases – are common to all capacitors.



A dielectric is an insulator; when placed between the plates of a capacitor it gives a lower potential difference with the same charge, due to the polarization of the material. This increases the capacitance.



The polarization of the dielectric results in a lower electric field within it; the new field is given by dividing the original field by the dielectric constant κ:

Therefore, the capacitance becomes:



The dielectric constant is a property of the material; here are some examples:



If the electric field in a dielectric becomes too large, it can tear the electrons off the atoms, thereby enabling the material to conduct. This iscalled dielectric breakdown; the field at which this happens is called the dielectric strength.


20‐5 Capacitors and Dielectrics








20-6 Electrical Energy Storage

By considering how much energy it takes to move an increment of charge, ΔQ, from one plate to the other, we can find the total energy stored in the capacitor:


20-6 Electrical Energy Storage

The energy stored in a capacitor can be put to a number of uses: a camera flash; a cardiac defibrillator; and others. In addition, capacitors form an essential part of most electrical devices used today.

If we divide the stored energy by the volume of the capacitor, we find the energy per unit volume; this result is valid for any electric field:


20‐6 Electrical Energy Storage


20‐6 Electrical Energy Storage


Summary of Chapter 20

• Electric force is conservative, and has a potential energy associated with it

• Change in electric potential energy:

• Change in electric potential:

• Relation between electric field and electric potential:

• Total energy (electric potential energy plus kinetic energy) is conserved



• Positive charges accelerate in the direction of increasing potential

• Negative charges accelerate in the direction of decreasing potential

• Electric potential of a point charge:

• Electric potential energy of two point charges:

• Total electric potential and total electric potential energy are sums of those due to individual charges



• Equipotential surfaces are those on which the electric potential is constant.

• The electric field is perpendicular to the equipotential surfaces.

• Ideal conductors are equipotential surfaces.

• A capacitor is a device that stores electric charge.

• Capacitance:



• Capacitance of a parallel-plate capacitor:

• A dielectric is an insulator that increases a capacitor’s capacitance.

• A dielectric is characterized by its dielectric constant.

• A sufficiently large electric field can cause a dielectric to break down.



• A capacitor also stores electric energy.

• Electric energy stored in a capacitor:

• Energy density in an electric field:

Chapter 20

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