Physics Lab 202P-4 Understanding Electric Potential NAME: LAB PARTNERS: LAB SECTION: LAB INSTRUCTOR: DATE: EMAIL ADDRESS: Penn State University Created by nitin samarth Physics Lab 202P-4 Page 1 of 17
Physics Lab 202P-4 Equipment List (all items marked with * are in the student kit, others are supplied at the time of the lab) Equipotential plotting kit (conductive ink pen, coated paper, board, stencil, pushpins) 5V DC power supply Digital voltmeter Probes and hook-up wires Computer Software List EMField Penn State University Created by nitin samarth Physics Lab 202P-4 Page 2 of 17
Prelab checkbox: Satisfactory Unsatisfactory Physics Pre-lab 202P-4 Understanding Electric Potential Name: Section: Date: (Read this & answer the questions before coming to lab) Summary of relevant concepts: (a) The ELECTRIC POTENTIAL ENERGY U of a charge at any point in space is defined as the NEGATIVE of the work done BY the electric field E when the charge is moved from infinity to that point. Here, we DEFINE the electric potential at infinity to be 0. Note that this definition is equivalent to saying: "electric potential energy is the work YOU have to do in bringing a charge from infinity to that point." (b) The ELECTRIC POTENTIAL V at any point in space is defined as the negative of the work done by the electric field when a charge of +1 C is brought from infinity to that point i.e. V = A r r E ds (c) We also talk about the POTENTIAL DIFFERENCE between two points A & B: B = r V E r ds i.e. the negative of the work done by the electric field in moving a charge of +1C from A to B. (d) Electric potential and potential difference are measured in VOLTS; electric potential energy is measured in joules. (e) Equipotential surfaces are a convenient way of picturing the electric potential in any region. Most often, equipotential LINES are used to portray a cross-sectional view of equipotential surfaces. By definition, all points on an equipotential line/surface have the same potential. A Penn State University Created by nitin samarth Physics Lab 202P-4 Page 3 of 17
Pre-lab Questions: Q1. What is a "conservative force?" (Recall: Physics 201.) Q2. When a mass that is free to move is released in the presence of a gravitational field, does it move from a region of high gravitational potential to a region of low gravitational potential or vice-versa? Q3. When a CHARGE that is free to move is released in the presence of an electric field, does it move from a region of high electric potential to a region of low electric potential or vice-versa? Does your answer depend on whether the charge is positive or negative? Why/why not? Penn State University Created by nitin samarth Physics Lab 202P-4 Page 4 of 17
The figure below shows a region of space with a uniform electric field E. You can move charges from A to B along the three different paths shown. ACBD is a square of side L. Q4. Suppose a positive charge +q is moved from A to B. Calculate the work W done by the electric field on the charge, if the charge +q were taken: (a) first from A to C and then from C to B. (b) first from A to D and then from D to B. (a) (b) Penn State University Created by nitin samarth Physics Lab 202P-4 Page 5 of 17
Q5. Calculate the work done by the electric field on the charge if the charge were moved along the straight line AB. How does this compare with your answers to Q4? Q6. From your answers to Q4 & Q5, what is the "the potential difference" DV = V B - V A between points A and B? Q7. An equipotential surface is defined as a surface on which there is no potential difference between any of the points. What are the equipotential surfaces for the problem above? Sketch a cross-sectional view of a few equipotential surfaces, showing surfaces with a constant potential difference between them. Penn State University Created by nitin samarth Physics Lab 202P-4 Page 6 of 17
Q8. You have already learned that -- under conditions of STATIC EQUILIBRIUM (i.e. no charges are moving) -- the electric field at the surface of any conductor is PERPENDICULAR to the surface. You also know that the electric field inside a solid conductor is ZERO. So, how much work do you have to do in moving a test charge from one point on a conductor to any other point on that conductor? What does this tell you about the POTENTIAL at all regions of a conductor? Penn State University Created by nitin samarth Physics Lab 202P-4 Page 7 of 17
(This page is left purposely blank) Penn State University Created by nitin samarth Physics Lab 202P-4 Page 8 of 17
Lab Activity: Understanding Equipotentials (A Real Experiment with a Virtual Interlude.) This lab involves two separate activities: A real experiment in which you will measure the electric potential in and around a charged "hollow" conductor A virtual experiment in which you simulate the electric potential from an electric dipole. It will be necessary to set up the real experiment first. Then, while the conductive ink is drying, you should go ahead and finish the simulation and return to the first activity: you will have to wait at least 20 minutes for the experiment to work properly. Just follow the instructions in the sequence given. I. Measuring the potential in, on and around a hollow conductor: setting the stage. Important Note: this experiment uses a conductive paint that should be used with common sense and ONLY as directed. i. Please use the disposable gloves provided when handling the paint. ii. Avoid getting the paint on your skin. iii. Do NOT get the silver paint in your eyes. (a) Th experiment makes use of the field plotting kit provided in lab. Place a sheet of conductive paper, printed side up, on a smooth hard surface. DO NOT attempt to draw the conductive electrodes while the paper is on the corkboard. (b) Shake the conductive pen (with the cap on) vigorously for 10-20 seconds to disperse any particle matter suspended in the ink. (c) Remove the cap. Press the spring loaded tip lightly down on a piece of dark, scrap paper. If you now squeeze the pen barrel firmly, you will start the ink flowing. Draw the pen slowly across the scrap paper and you should get a solid silver/white line. The width of the line is determined by how fast you move the pen and how hard you press down. (d) Once you are satisfied that you can get this to work, it's time to draw an electrode on the conductive paper. Using the stencil, draw a circle of diameter 1.25" in the center of the paper. Then, draw a concentric circle of diameter 1.5" around the smaller circle. Use the pen to carefully shade the region between the two circles, forming a conducting "shell." Your pattern should be solid and not have spaces and holes. The experiment works best once the ink is dry and has maximum conductivity. This will take about 20 minutes. Set the conductive paper aside and go on to the next activity for now. Penn State University Created by nitin samarth Physics Lab 202P-4 Page 9 of 17
II. Visualizing the electric potential created by a dipole: A Virtual Interlude. EMFIELD can be used to get some insights into the electric potential created by arrangements of point charges. We'll use our favorite one: the electric dipole. Start EMField from the Physics program group under the START menu. From the "Display" menu, select "Show grid" and "Constrain to grid"; From the "Sources" menu, select "3D point charges;" From the array of positive and negative charges at the bottom of the screen, select a positive charge of +4 units and drag it to a position somewhere near the middle of the screen. Select a negative charge of -4 units and position it 4 horizontal units from the positive charge. First, try to get a feeling for the values of the electric potential created by this electric dipole. To do this, from the "Fields and potential" menu, select the "Potential" option. If you click the mouse button down, the program will show a number that is proportional to the electric potential V at that point on the screen. The units in this program are of course arbitrary, but for convenience, we'll refer to them as "volts." Next, from the "Fields and potential" menu, select the "Equipotentials with number" option. If you click the mouse button down, the program will draw an equipotential passing through a given point on the screen. The line is labeled with a number that represents the electric potential V. Now, choose the "potential difference" option from the menu. This allows you to drag any path on the screen and calculates the potential difference between the starting position and the endpoint of the path. Try three different paths that begin and end at the same points and note how the potential difference varies with the choice of path. Finally, choose a path that approximately follows one of the equipotentials and confirm that the program indeed does make sense. Q1. Use the program to make a plot that shows equipotentials for the elctric dipole with the following values: V = -3.2 V, -1.5 V, -0.7 V, -0.3 V, 0 V, +0.3 V, +0.7 V, +1.5 V, +3.2 V. (In case you cannot match these values exactly, don't worry about it. Get as close as you can.) In this plot, also show a few electric field lines. Print this figure and include it with your report. Penn State University Created by nitin samarth Physics Lab 202P-4 Page 10 of 17
Now, refer to your equipotential and electric field line plot, as well as to the exercises you carried out above, and answer the following questions. Q2. Do you notice any obvious geometrical relationship between equipotentials and electric field lines? Describe this relationship and why it makes sense. (Think about the direction of the electric field and the work done in moving a charge along an equipotential.) Q3. If you were to bring a positive charge from infinity to ANY point on the perpendicular bisector of the electric dipole following an ARBITRARY path, how much work would you do? Justify your answer using your equipotential plot. Penn State University Created by nitin samarth Physics Lab 202P-4 Page 11 of 17
Q4. Is it true that wherever the electric potential V = 0, the electric field E is also 0? Justify/support your answer using information on your plot. Q5. Is it true (in general) that wherever the electric field E = 0, the electric potential V is also 0? Suggest an arrangement of charges that would help justify your answer. Penn State University Created by nitin samarth Physics Lab 202P-4 Page 12 of 17
Q6. Suppose you released a POSITIVE charge from a point located on the +0.3 V equipotential. Would it move to a point of higher POTENTIAL or lower POTENTIAL? Would it move to a point of higher POTENTIAL ENERGY or lower POTENTIAL ENERGY? Justify your answers based on the electric field lines in your plot. Q7. Suppose you released a NEGATIVE charge from a point located on the +0.3 V equipotential. Would it move to a point of higher POTENTIAL or lower POTENTIAL? Would it move to a point of higher POTENTIAL ENERGY or lower POTENTIAL ENERGY? Justify your answers using the electric field lines in your plot. Penn State University Created by nitin samarth Physics Lab 202P-4 Page 13 of 17
III. Back to the Hollow Conductor: A Return to (Messy) Reality. Simulations are great fun, but physics deals with the real world! So, let's get on with an experiment that examines the electric potential in and around a charged conductor. The principal equipment you need for the experiment consists of a 5 V DC power supply, a digital voltmeter, and the graphite paper on which you drew the conductive pattern. Keep in mind that the graphite paper is a slightly conductive paper and does in fact carry a small current (moving charge) when you apply a battery across it. So, even this experiment is not an accurate representation of static equilibrium! But, it actually works quite well. DC Power Supply Power Low voltage Com +5V Hi probe Digital voltmeter 5.03 Set to 20V On/off DC Input Lo Hi Lo probe First, position your paper (with the circle pattern facing up) on the corkboard provided. Fasten the paper to the corkboard using pushpins. Next, use a pushpin to connect a wire to a point on your silver circle; use a pushpin to connect another wire to a point on the periphery of the graphite paper. Make sure that the pushpins make good contact between the metal connector at the end of the wire and the silver pattern. Make sure the power supply is connected to the mains, with the power switch OFF. Connect the wire from the silver circle to the +5V output of the power supply. Connect the wire from the edge of the graphite paper to the "COM" output on the power supply (this refers to "common" or "ground" and provides a reference for 0 V). Turn the power ON and also turn the "low voltage" switch ON. Next, make sure the digital voltmeter is connected to its power supply. Set up the digital multimeter to read DC Volts by depressing the "V" button. Follow the gold path from the "V" to find the button that corresponds to a maximum voltage reading of 20 V. Depress that button. The digital voltmeter should have two probes plugged into its input: a red one and a black one. Place the black probe firmly in contact with the connector at the edge of the paper. Penn State University Created by nitin samarth Physics Lab 202P-4 Page 14 of 17
Make sure you contact the metal connector at the end of the wire, not the head of the pushpin. While the black probe is held in place, the red probe can now be used to read the potential at different places on the graphite paper. Answer the following questions: Q8. How does the potential vary when you probe different locations on your silver ring? What we expected and why: What we observed and why: Penn State University Created by nitin samarth Physics Lab 202P-4 Page 15 of 17
Q9. How does the potential vary with position outside the silver ring? For instance, how does it change with the distance from the center of the ring? Use a sketch to show, approximately, what the equipotentials look like? What we expected & why: What we observed and why: Penn State University Created by nitin samarth Physics Lab 202P-4 Page 16 of 17
Q10. How does the potential vary at different positions INSIDE the silver ring? What we expected and why: What we observed and why: Penn State University Created by nitin samarth Physics Lab 202P-4 Page 17 of 17