Chapter 20 Electric Potential and Electric Potential Energy

Units of Chapter 20 Electric Potential Energy and the Electric Potential Energy Conservation The Electric Potential of Point Charges Equipotential Surfaces and the Electric Field Capacitors and Dielectrics Electrical Energy Storage

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:

20-1 Electric Potential Energy and the Electric Potential 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:

20-1 Electric Potential Energy and the Electric Potential The electric field is related to how fast the potential is changing:

20-2 Energy Conservation In 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 of decreasing electric potential; Negative charges accelerate in the direction of increasing electric potential. In both cases, the charge moves to a region of lower potential energy.

20-3 The Electric Potential of Point Charges The difference in potential energy between points A and B is

20-3 The Electric Potential of Point Charges Therefore, the electric potential of a point charge is: shown here for a positive and negative charge, respectively

20-3 The Electric Potential of Point Charges The electric potential of a group of point charges is the algebraic sum of the potentials of each charge.

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.

20-4 Equipotential Surfaces and the Electric Field 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.

20-4 Equipotential Surfaces and the Electric Field For two point charges:

20-4 Equipotential Surfaces and the Electric Field 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.

20-4 Equipotential Surfaces and the Electric Field 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:

20-4 Equipotential Surfaces and the Electric Field 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: 20-5 Capacitors and Dielectrics

A simple type of capacitor is the parallel-plate capacitor. It consists of two plates of area A separated 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:

20-5 Capacitors and Dielectrics 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.

20-5 Capacitors and Dielectrics 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.

20-5 Capacitors and Dielectrics 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:

20-5 Capacitors and Dielectrics The dielectric constant is a property of the material; here are some examples:

20-5 Capacitors and Dielectrics 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 is called dielectric breakdown; the field at which this happens is called the dielectric strength.

20-6 Electrical Energy Storage By considering how much energy it takes to move an increment of charge, Δ Q, 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:

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

Summary of Chapter 20 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

Summary of Chapter 20 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:

Summary of Chapter 20 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.

Summary of Chapter 20 A capacitor also stores electric energy. Electric energy stored in a capacitor: Energy density in an electric field: