Chapter+19

toc __**Chapter 19: Electrical Potential and Capitance**__

=Guiding Questions= > Energy is the capacity of something to perform work > Work is performed when a force acts upon an object to cause displacement > Energy is always conserved when it changes forms. > Conservative – the energy of the work performed is stored. > Non-conservative – the energy of the work performed is not stored. > Electrostatic force is the attraction or repulsion between two objects > Conservative 6. What is the definition of potential difference? What is the equation, symbol and unit of potential difference? Why is potential difference a relative value, not an absolute value? a. When work is done on a charge, its potential energy is changed to a higher value. Now there is a difference of electrical potential energy between the two locations that the charge was at. This change is potential difference.
 * 1) Review what you know about energy from last year’s notes! Also look in the Cutnell and Johnson text and on The Physics Classroom.
 * 2) What is energy?
 * 1) What is work?
 * 1) When is energy conserved?
 * 1) What is the difference between conservative and non-conservative types of forces and energies?
 * 1) What is electrostatic force? Is it conservative or nonconservative?
 * 1) Combine the equations for work and for electric field strength to get a new expression for work.
 * 2) W = E*q*d
 * 3) In a uniform electric field, a charge moves from one place to another. What are the only types of energy present in this situation?
 * 4) Kinetic and Electrical Potential Energy
 * 5) Use this to find an expression for the change in potential energy.
 * 6) Change in PE = Eqd
 * 7) Check this out! Real footage of So Cal Edison opening a switch on a 500kV line while its under load to make repairs. Turn it up, the sound is cool. []
 * 8) Pretty cool.

7. A uniform electric field of magnitude 250 V/m is directed in the positive x direction. A +12-μC charge moves from the origin to the point (20-cm, 50-cm). What was the change in the potential energy of this charge? Through what potential difference did the charge move?

 b. Voltage. It can be positive or negative.

**Summary - Lesson 1**


 * Electric Field and the Movement of Charge **

Action-at-a-distance forces are sometimes referred to as field forces. The space surrounding a charged object is affected by the presence of the charge; an electric field is established in that space. A charged object creates an electric field - an alteration of the space or field in the region that surrounds it.


 * Electric Field, Work, and Potential Energy **

Summed up by these two pictures






 * Electric Potential **

Electric Potential Energy is dependent on two things:

1) Electric charge - a property of the object experiencing the electrical field, and

2) Distance from source - the location within the electric field

Electric potential is the potential energy per charge. The concept of electric potential is used to express the affect of an electric field of a source in terms of the location within the electric field.




 * Electric Potential Difference **

By definition, the electric potential difference is the difference in electric potential (V) between the final and the initial location when work is done upon a charge to change its potential energy. In equation form, the electric potential difference is



Unit of electrical potential difference is the volt, V. One Volt is equivalent to one Joule per Coulomb.


 * Electric Potential Difference and Simple Circuits **

As the positive test charge moves through the //external circuit// from the positive terminal to the negative terminal, it decreases its electric potential energy and thus is at low potential by the time it returns to the negative terminal. If a 12 volt battery is used in the circuit, then every coulomb of charge is gaining 12 joules of potential energy as it moves through the battery. And similarly, every coulomb of charge loses 12 joules of electric potential energy as it passes through the external circuit. The loss of this electric potential energy in the external circuit results in a gain in light energy, thermal energy and other forms of non-electrical energy.

The cells simply supply the energy to do work upon the charge to move it from the negative terminal to the positive terminal. By providing energy to the charge, the cell is capable of maintaining an electric potential difference across the two ends of the external circuit. Once the charge has reached the high potential terminal, it will naturally flow through the wires to the low potential terminal. In a battery-powered electric circuit, the cells serve the role of the charge pump to supply energy to the charge to lift it from the low potential position through the cell to the high potential position.

The ** internal circuit ** is the part of the circuit where energy is being supplied to the charge. The ** external circuit ** is the part of the circuit where charge is moving outside the cells through the wires on its path from the high potential terminal to the low potential terminal.

= Notes =

= Equipotential Lab =

What is the relationship between electric field lines and equipotentials?

|| Volt meter (VOM)
 * Expected Materials ** :
 * Alligator leads (2) || Metal push pins (2) ||
 * Cork board || Power supply || Silver marker ||

**Preparing the materials**
1) Select a sheets with silver conductive lines drawn on it. Use a conductive ink pen to draw one of the given shapes.

2) Place the sheet on the cork pad. Place one metal pin through each of the two painted silver points on the conducting paper.

3) Insert black probe in to COM socket of the voltmeter (VOM) and insert red probe into other Voltmeter socket. Then, set selector to 20V.

4) Set power supply to 20V. Test power supply with VOM to make sure that it is working.

5) Attach one lead wire from the power supply to one metal pin, then attach another wire from the other clip of the power supply to the second metal pin on the corkboard.

6) Attach the black COM wire from the voltmeter to one of the pins.

**//Recording data//**
7) Create a numbered grid in Excel using the conducting sheet as a reference.

8) You will only do points 5 to 15 on the vertical axis, and 5 to 20 on the horizontal axis.

9) Touch the red wire from the voltmeter gently to point (5,5). Use the first number that appears on the voltmeter. Enter your data directly into Excel. Move to the next point (5,6). Repeat for all points until you reach (15, 20).

10)Repeat for the other designs.


 * //Graphing Data//**

11)Highlight entire table

12)Graph a SURFACE

13)Create two views: Side and Top

14)Adjust scale to “2”. (It does “5” as a default.)

15)If graph is not relatively smooth, go back and remeasure.

16)Put your name(s), lab title, and date on the header/footer.

17)Email me a copy of your Excel document and I will compile all of them into one document and email them to everyone.


 * Prelab: **
 * 1) The objective is stated in the title. What is your hypothesis?
 * 2) The equipotentials will be the same distance from the charge, creating certain shapes. The positive areas will have higher voltage and the opposite will be true for the negative areas. This will be shown by electric field lines moving from high voltage to low voltage.
 * 3) What is the rationale for your hypothesis?
 * 4) The definition of equipotential is my evidence because the same charges will be at an equal distance from the source. Also, the negative areas will have a lower charge because when particles reach their destination of the negative source, their electric potential will decrease.
 * 5) How do you think you might test this hypothesis?
 * 6) We will use a board and put two charges on the board, and then find out charges on specific points.
 * 7) Predict the electric field lines (and the equipotential surfaces) of the following situations:
 * 8) Two point sources (one negative and one positive)
 * 9) [[image:Photo_on_2011-09-26_at_15.23.jpg width="305" height="229"]]
 * 10) A circle (negatively charged) and a positive point charge in the very center of it.
 * 11) [[image:Photo_on_2011-09-26_at_15.24.jpg width="318" height="240"]]
 * 12) Two lines of charge (one negative and one positive)
 * 13) [[image:Photo_on_2011-09-26_at_15.24_#2.jpg width="329" height="249"]]

Graphs



 * Dipole**



Top View Side View Cool View Done by Sam Fihma, Steven Thorwarth, and Phil Litmanov This shows the two source charges at the top of the mountain (positive) and the bottom of the valley (negative). Each shade of colors shows the equipotentials and it is clear that the charges continually decrease.


 * Parallel Plates**



Top View Cool View Done by Richie Johnson, Bret Pontillo, and Allison Irwin This shows the two source charges as parallel lines and the shape the equipotentials created as a result.


 * Two Positive Charges**



Top View Side View This was done by Eric Solomon, Chris Hallowell, and Ryan Listro. The two positive sources are shown at the peak of the mountains. The equipotentials create "waves" that can be seen as concentric circles.


 * Circle**



Top View Side View This was done by Erica Levine, Ross Dember, and Rebecca Rabin. The peak of the mountain represents the positive charge in the center of the ring. The equipotentials are concentric circles around this charge, but they decrease showing that as they get further form the positive source, they have less of a charge.


 * Electric Field Lines**

Dipole These lines wiggle immensely, but the basic flow of the lines is correct. They should come out of the positive charge and enter into the negative charges. There should also be lines that start to curve towards the negative charge, but take a wider path to reach it. What it is not drawn on this, but what should be drawn, are more lines that are not from the positive charge funneling into the negative charge.

Parallel Plates These lines match up perfectly with the theoretical picture. The lines are supposed to come from one of the plates and travel to the other (positive to negative). The lines on the other side should emerge from the line and start to curve a bit towards the other plate.

Two Positive Charges This picture is very similar to what it should look like in theory. If perfect, the lines would not wiggle as much and would be nice and smooth, but that is not the case. Other than this, it is basically the same. The lines are supposed to emerge from the charge and then quickly curve away from the other one.

Circle This one is nearly perfect. The lines from the positive charge travel in a perpendicular line (perpendicular to the surface of the original charge, like the others too) to the negative circle. In theory, the lines should look like this too. However, the equipotential levels would be more circular than they are in this picture.

Conclusion
The four graphs our class plotted was the Dipole, Two Positive Charges, Parallel Plates, and a Circle. In each graph, there are equipotential levels and electric field lines moving away from the positive regions and into the negative regions. These electric field lines are lined up perpendicularly with the equipotential levels. The dipole graph has electric field lines moving away from the positive source and right into the negative source. The two positive charges graph shows lines moving away from both positive charges and off the graph. It is clear they are trying to avoid the other positive source. The parallel plates graph shows the lines clearly moving into the negative source charge. The circle graph has the lines moving away from the center positive charge and to the circular, negative region. Looking at the analysis I did where I drew the electric field lines using the equipotential levels, I believe the class did well. The path of the lines came out basically how they theoretically were supposed to. It is clear they are not perfect though. The lines should be nice and smooth, but they are not, due to the fact that the equipotential levels are not perfectly even like they should be. My hypothesis seems to be correct. The electric field lines did move from regions of positive to negative. However, I did not include the fact that the lines have to be perpendicular with the equipotential levels. I was right though about the shapes the equipotentials would make. The biggest possible source of error my group found was the difference in readings based on the amount of pressured you applied to the chart. In order for it to be perfect, you would need to apply the same pressure to each point, which is impossible. Also, the readings jumped around often. At one point it could read 9 V, while a second later it could read 12 V. The readings were definitely hard to measure and this was our biggest source of error. If we were to do this lab over, a better device to read the voltages would be needed. This would greatly reduce the error of all groups.


 * Note:** Resubmitted work includes procedure, data tables, and more analysis that is written below each picture I drew.