Chapter 17 Electric Potential

Units of Chapter 17 Electric Potential Energy and Potential Difference Relation between Electric Potential and Electric Field Equipotential Lines The Electron Volt, a Unit of Energy Electric Potential Due to Point Charges Potential Due to Electric Dipole; Dipole Moment

Units of Chapter 17 Capacitance Dielectrics Storage of Electric Energy Cathode Ray Tube: TV and Computer Monitors, Oscilloscope The Electrocardiogram (ECG or EKG)

Objectives: The students will be able to: Distinguish between electric potential, electric potential energy, and electric potential difference. Draw the electric field pattern and equipotential line pattern which exist between charged objects. Determine the magnitude of the potential at a point a known distance from a point charge or an arrangement of point charges. State the relationship between electric potential and electric field and determine the potential difference between two points a fixed distance apart in a region where the electric field is uniform.

Electric Fields and WORK In order to bring two like charges near each other work must be done.   In order to separate two opposite charges, work must be done.  Remember that whenever work gets done, energy changes form. As the monkey does work on the positive charge, he increases the energy of that charge.  The closer he brings it, the more electrical potential energy it has.   When he releases the charge, work gets done on the charge which changes its energy from electrical potential energy to kinetic energy.  Every time he brings the charge back, he does work on the charge.  If he brought the charge closer to the other object, it would have more electrical potential energy.  If he brought 2 or 3 charges instead of one, then he would have had to do more work so he would have created more electrical potential energy.  Electrical potential energy could be measured in Joules just like any other form of energy.

Electric Fields and WORK Consider a negative charge moving in between 2 oppositely charged parallel plates initial KE=0 Final KE= 0, therefore in this case Work = DPE We call this ELECTRICAL potential energy, UE, and it is equal to the amount of work done by the ELECTRIC FORCE, caused by the ELECTRIC FIELD over distance, d, which in this case is the plate separation distance. Is there a symbolic relationship with the FORMULA for gravitational potential energy?

Electric Potential Here we see the equation for gravitational potential energy. Instead of gravitational potential energy we are talking about ELECTRIC POTENTIAL ENERGY A charge will be in the field instead of a mass The field will be an ELECTRIC FIELD instead of a gravitational field The displacement is the same in any reference frame and use various symbols Putting it all together! Question: What does the LEFT side of the equation mean in words? The amount of Energy per charge!

Change in electric potential energy

For a positive test charge to be moved upward a distance d, the electric force does negative work. The electric potential energy has increased and U is positive (U2 > U1)

If a negative charge is moved upward a distance d, the electric force does positive work. The change in the electric potential energy U is negative (U2 < U1)

Energy per charge Video The amount of energy per charge has a specific name and it is called, VOLTAGE or ELECTRIC POTENTIAL (difference). Why the “difference”? Video

Understanding “Difference” Let’s say we have a proton placed between a set of charged plates. If the proton is held fixed at the positive plate, the ELECTRIC FIELD will apply a FORCE on the proton (charge). Since like charges repel, the proton is considered to have a high potential (voltage) similar to being above the ground. It moves towards the negative plate or low potential (voltage). The plates are charged using a battery source where one side is positive and the other is negative. The positive side is at 9V, for example, and the negative side is at 0V. So basically the charge travels through a “change in voltage” much like a falling mass experiences a “change in height. (Note: The electron does the opposite)

17.1 Electrostatic Potential Energy and Potential Difference The electrostatic force is conservative – potential energy can be defined Change in electric potential energy is negative of work done by electric force: (17-1)

17.1 Electrostatic Potential Energy and Potential Difference Electric potential is defined as potential energy per unit charge: (17-2a) Unit of electric potential: the volt (V). 1 V = I J/C.

BEWARE!!!!!! W is Electric Potential Energy (Joules) is not V is Electric Potential (Joules/Coulomb) a.k.a Voltage, Potential Difference

The “other side” of that equation? Since the amount of energy per charge is called Electric Potential, or Voltage, the product of the electric field and displacement is also VOLTAGE This makes sense as it is applied usually to a set of PARALLEL PLATES. DV=Ed E DV d

17.1 Electrostatic Potential Energy and Potential Difference Only changes in potential can be measured, allowing free assignment of V = 0. (17-2b)

17.1 Electrostatic Potential Energy and Potential Difference Analogy between gravitational and electrical potential energy: a) Two rocks are at the same height. The larger rock has more potential energy. They have the same gravitational potential, biut the larger rock has the greater potential energy because it has more mass. (b) Two charges have the same electric potential. The 2Q charge has more potential energy.

The work done by an electric field to move a (+) particle q from A to B is equal to the negative change in potential energy. Note: next slide shows the equation

17.2 Relation between Electric Potential and Electric Field Work is charge multiplied by potential: Work is also force multiplied by distance: The work done by an electric field to move a (+) particle q from A to B is equal to the negative change in potential energy. The work done by an electric field to move a (+) particle q from A to B is equal to the negative change in potential energy.

Electric Potential (V) Electric potential is hard to understand, but easy to measure. We commonly call it “voltage”, and its unit is the Volt. 1 V = 1 J/C Electric potential is easily related to both the electric potential energy, and to the electric field.

The change in potential energy is directly related to the change in voltage. DU = qDV DV = DU/q DU: change in electrical potential energy (J) q: charge moved (C) DV: potential difference (V) All charges will spontaneously go to lower potential energies if they are allowed to move.

Sample Problem: A 3.0 μC charge is moved through a potential difference of 640 V. What is its potential energy change?

Sample Problem: A 3.0 μC charge is moved through a potential difference of 640 V. What is its potential energy change?

17.2 Relation between Electric Potential and Electric Field Solving for the field, Period 1 Start here (17-4b) If the field is not uniform, it can be calculated at multiple points:

Sample Problem: An electric field is parallel to the x-axis Sample Problem: An electric field is parallel to the x-axis. What is its magnitude and direction if the potential difference between x =1.0 m and x = 2.5 m is found to be +900 V?

Sample Problem: An electric field is parallel to the x-axis Sample Problem: An electric field is parallel to the x-axis. What is its magnitude and direction if the potential difference between x =1.0 m and x = 2.5 m is found to be +900 V?

Sample Problem Period 5 starts here

Sample Problem: If a proton is accelerated through a potential difference of 2.000 V, what is its change in potential energy?      How fast will this proton be moving if it started at rest?

Q1 is -3uC Q2 is 2uC Q3 is 4uC Skip right now

17.3 Equipotential Lines An equipotential is a line or surface over which the potential is constant. Electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential. Lines that represent the electric potential. Any point along a surface these lines must be perpendicular to the electric field.

17.3 Equipotential Lines Unlike electric field lines, which start and end on electric charges, equipotential lines and surfaces are always continuous and never end, and so continue beyond the borders. Field lines are in red and equipotential lines are in green.

Figure 17-8 Topographic map A topographic map (here, a portion of the Sierra Nevada in California) shows continuous contour lines, each of which is at a fixed height above sea level. Here they are at 80-ft (25-m) intervals. If you walk along one contour line, you neither climb nor descend. If you cross lines, and especially if you climb perpendicular to the lines, you will be changing your gravitational potential (rapidly, if the lines are close together). Contour lines are essentially gravitational equipotential lines.

Electric Field and Electric Potential E = - V / d Two things about E and V: The electric field points in the direction of decreasing electric potential. The electric field is always perpendicular to the equipotential surface.

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. There can be no electric field within a conductor in the static case, for otherwise the free electrons would feel a force and would move. Indeed a conductor must be entirely at the same potential in the static case, and the surface of a conductor is then an equipotential surface. If it weren’t the free electrons at the surface would move, since whenever there is a potential difference between two points, work can be done on charged particles to move them. This is consistent that the electric field at the surface of a conductor must be perpendicular to the surface.

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. Cardiac Cycle Electrical System of the Heart

Equipotential Surfaces and the Electric Field An electroencephalograph measures the electrical activity of the brain:

17.4 The Electron Volt, a Unit of Energy One electron volt (eV) is the energy gained by an electron moving through a potential difference of one volt.

Practice Problem 1: page 489 #2

Practice Problem 1: page 489 #2

Practice Problem 2: page 489 #5 How strong is the electric field between two parallel plates 5.8 mm apart if the potential difference between them is 220 V?

Practice Problem 2: page 489 #5 How strong is the electric field between two parallel plates 5.8 mm apart if the potential difference between them is 220 V?

pHET activity – Exploring Electric Potential, Electric Field and Distance Relationships Note: When finished go to http://vnatsci.ltu.edu/s_schneider/physlets/main/equipotentials.shtml and experiment with the various charge configurations. (written on hand-out)

Homework Complete computer activity responses. P.488 Questions #1, 2, 3 P. 489 Problems # 1, 3, 6, 7, 9

Question 1 answer

Question 2 Answer

Question 3 Answer

Closure Kahoot