* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Materials
Survey
Document related concepts
Transcript
PHYS 1402 – General Physics II Introduction to Electric Potential and E-field Mapping Leader: _____________________________ Recorder: ___________________________ Skeptic: _____________________________ Encourager: _________________________ Materials Part I 2 x D cells Pasco circuit kit Socket with 3 V light bulb 4 x Alligator clip wire Steel wool Genecon Digital Multimeter Part II Electric Field Mapping Apparatus with parallel plates 3 x Point Probes Battery Eliminator DMM 2 Sheets Quadrille Graph paper 4 x Banana plug cables Ruler Safety If the D cells used in the following procedure ever got noticeably hot, immediately disconnect any wires. Introduction In the first part of this activity we will investigate the idea of electric potential and its relation to electrical energy. We will also use a DMM to measure electric potential and observe the behavior of batteries when connected in series and parallel. In the second part of the activity we will investigate the connection between electric potential and the electric field by measuring surfaces of constant electric potential – called equipotential surfaces – and using them to determine the electric field in a parallel plate capacitor. Part I – Introduction to Potential Procedure Part 1 – Energy Transformations Make sure that the cord is plugged into the Genecon, and turn the handle of the Genecon at about 1 turn per second. Note: Do not turn the handle of the Genecon too hard as this can strip the gears inside. Q1) What type of energy does the Genecon handle have while you are turning it? Q2) From where did it obtain the energy? Connect the alligator clips on the cord together and turn the handle of the Genecon at about 1 turn per second. Q3) Did you have to exert a greater torque on the handle to turn it at the same rate when the leads were connected together? Q4) If you turn the handle at the same rate, does its kinetic energy change? Q5) If you had to exert a greater torque, then did you have to do more work on the Genecon? Clearly, when you connect the leads from the Genecon together, the amount of work you have to do increases, suggesting that the energy you are adding to the system is being dissipated, but as what? Disconnect the alligator clips and connect them on opposite sides of a single strand of steel wool. Give the Genecon a couple of quick turns and observe what happens. If nothing happens, make sure that the connection to the steel wool is good. If nothing happens after several tries, contact your instructor. Q6) Describe what you observed. Q7) What was the source of the thermal energy that melted the strand of steel wool? (I.e. where was the energy input?) Connect the Genecon leads to opposite sides of the provided light bulb socket. Turn the handle at about 1 turn per second and observe what happens. Note if the handle turns very easily and nothing happens check your connections. If still nothing happens contact your instructor. Q8) Describe what you observe. Q9) How is the light bulb lighting similar to the strand of steel wool melting? How is it different? Q10) What was the source of the thermal energy that causes the light bulb to glow? (I.e. where was the energy input?) As a historical note, Edison’s invention of the light bulb was not really the discovery that if metal got really hot it glowed. The invention was finding a practical light bulb that would last. You should have observed that you were doing work on the handle and that the work you did was being dissipated as heat by the light bulb. The Genecon is an energy conversion device. It converts the mechanical energy of turning the handle into electrical energy. The electrical energy is transmitted by charge flowing in the wire. Q11) What does the light bulb do to the electrical energy? Part 2 – Potential Difference Place one of the D cells into a battery holder on the Pasco circuit board. The board has connections which are made by attaching wires to the coils on the board. Attach a wire from each side of the battery to a corresponding side of a light bulb socket. Disconnect the light bulb after you make your observation to preserve battery life. Q12) Describe what you see. Q13) From where did the light bulb obtain the energy to light? Q14) Did you do work on the battery so that it could provide the energy or was the energy already stored in the battery (by some previous work)? Q15) Another term for stored energy is __________ energy. It turns out to be convenient in electricity that instead of talking about potential energy, we refer to potential energy per charge. If a charge, q, experiences a difference in potential energy, ΔU, between two points, then the Potential Difference, ΔV, between those two points is defined as ΔV = ΔU/q. The SI unit for potential difference is the volt for which the symbol is V. Q16) If a battery is rated at 1.5 V, then across its terminals it provides 1.5 V of __________ ___________, or 1.5 joules of ________________ per coulomb of __________. Part 3 – Measuring Potential Difference In this part of the lab we will explore measuring potential difference and familiarize ourselves with the use of a digital multimeter, DMM. A DMM is probably the most basic tool for making electrical measurements. The DMM has several sockets into which you plug the wires – known as leads. You choose various sockets depending on what quantity you are measuring. You will always plug one of the leads into the socket labeled COM. COM stands for common since it is always used no matter what you measure with the DMM. To measure potential difference, plug the black lead into the socket marked COM and the red lead into the socket labeled V Ω. Turn on the DMM so that it will read DC volts. Simultaneously place the red lead on the + terminal of a D cell and the black lead on the – terminal of the same D cell. Q17) Record your reading. Don’t forget units. Q18) Reverse the side of the battery to which the leads are connected. How does the reading on the DMM change? A DMM when set up correctly is designed to that the lead connected to the V Ω socket is at a higher potential than the lead connected to the COM socket when the measured potential is positive. Q19) Which terminal of the battery is at higher potential. Explain using your answer to Q17 and Q18. Some DMMs can measure AC as well as DC potential. A common error in using DMMs with this capability is to have the DMM on the wrong setting when trying to measure a potential difference. Switch the DMM to the AC Volts setting and measure the potential difference across the battery. Q20) Record the result. Q21) If measuring a DC potential difference and you obtain 0 V, what is a good thing to check on the meter? Part 4 – Batteries in Series and Parallel Place a D cell into the second battery holder. Connect the + terminal of one cell to the – terminal of the second. Notice that the cells are connected one after the other. This type of connection is known as a series connection. When multiple cells are connected together, the combination is known as a battery. Q22) Which terminals will be the + and – terminals of the battery? Explain. Connect the battery across a light bulb. Q23) How does the brightness of the light bulb now compare to the brightness when it when it was connected to a single D cell? You may want to connect the light bulb across a single D cell again for reference. Q24) What does this suggest about the potential difference across a series combination of cells compared to an individual cell. Q25) Make sure that the DMM is on the DC setting and use it to measure the potential difference across the battery. Record the result. Q26) How does the measured potential difference of the battery compare to the measured potential difference of the individual cell? Get together with a nearby group and measure the potential difference for three cells connected in series and then four cells connected in series. Q27) Record your results. (Groups can separate now.) Q28) When cells are connected in series, the potential difference of the combination is the __________ of the individual potential differences. Now connect the cells so that the + terminals are connected to each other and – terminals are connected to each other. This combination of cells is referred to as a parallel combination. Connect the parallel combination across a light bulb. Q29) How does the brightness of the light bulb now compare to the brightness when it when it was connected to a single D cell? You may want to connect the light bulb across a single D cell again for reference. Q30) What does this suggest about the potential difference of a parallel combination compared to an individual cell? Q31) Which are the + and – terminals of a parallel combination of cells? Q32) Use the DMM to measure the potential difference across the parallel combination of cells. Record the result. Q33) When identical cells are connected in parallel, the potential difference of the combination is the ___________ of the individual cells. Note only identical cells should ever be connected in parallel. Q34) If we want a light bulb to be brighter we want to connect cells in __________. Q35) Most graphing calculators have four 1.5 V cells connected in series. What potential difference is the calculator using? We will discuss what applications there might be for connecting batteries in parallel at a later date. Part II – Mapping the Electric Field Introduction In part I we have explored the meaning of potential difference and learned how to measure it. In part II of this activity we will investigate the relationship between the electric field and potential difference. We will do so by using potential difference to map the electric field lines of a two-dimensional parallel plate capacitor. A parallel plate capacitor consists of two parallel conducting plates separated by a small distance. From the book we know that the magnitude of the average electric field between two points separated a distance x is given by Eave = V/x (1), where V is the potential difference between the two points. Thus by measuring the distance separating and the potential difference between two points, we can determine the magnitude of the average field. Q1) The electric field is a vector quantity, so to completely specify it what must we find besides the magnitude of the field? To find the direction, we first note that the average field between any two points where the potential difference is zero is also zero. An equipotential surface is a surface along which the potential is the same everywhere. Q2) What is the potential difference between any two points on an equipotential surface? Q3) What then is the average electric field between any two points on an equipotential surface? We define the direction of the average electric field as that in which the potential is changing most rapidly. This direction, it turns out, will always be perpendicular to the equipotential surfaces. Also, by definition electric field lines run from a region of higher potential to a region of lower potential. Thus, in this lab we will determine the electric field by finding equipotential surfaces. The magnitude of the field will be determined by measuring the potential difference and the distance between the equipotential surfaces, and the direction of the electric field will be obtained by determining the direction perpendicular to the equipotential surfaces. Q4) What is the static electric field inside a conductor in electrostatic equilibrium? Q5) If the static electric inside a conductor is 0, then is there a potential difference between any two points in a conductor in static equilibrium? Q6) Is a good conductor in electrostatic equilibrium an equipotential surface? Explain. In the procedure below, we will use the fact that a conductor in electrostatic equilibrium is an equipotential surface to help us map the electric field. Procedure The apparatus for this lab is sketched in figure 1. It consists of a plastic dish, several probes, several stainless steel metal strips, graph paper, a power supply (battery eliminator), and a digital multimeter (DMM). The DMM is an inexpensive and versatile instrument which can be used to measure resistance, AC and DC current, and AC and DC potential differences. 1. Set-up the Apparatus To set up the experiment, first determine the scale of the graph paper by measuring the spacing for 10 grid and divide by 10. Record the spacing between the grids on the graph paper in the space below. Spacing per grid = ________ cm/grid Next, place the graph paper underneath the dish so that the grid lines run parallel to the edges of the dish. Place the stainless strips with their long edges parallel to the long edges of the dish, and so that their inner edges are aligned along grid lines separated by 20 grid lines. Place the tip of two of the probes on each of the conductors. Fill the dish with water until the conductors are just covered by the water. Using the provided banana plug cables, connect the + terminal of the power supply to one of the probes and the terminal to the other probe. It is customary to use a red wire for the connection to the positive side, and a black wire for the connection to the negative side. Set the power supply to 6 V and turn it on. Figure 1 Schematic of experimental apparatus Power Supply DMM 2. Setup the DMM Connect each of the probes from the digital multimeter (DMM) to one of the remaining two probes. The connectors on the back of the probe will unscrew revealing a hole in the connector that you can put the probe into. Tighten down the connector to hold the probe and make a good contact. Turn the dial on the DMM to the 20 V DC setting. The DC side is indicated by a solid line over several dashed lines. Place the probe connected to the red probe on the DMM on the conductor connected to the plus side of the power supply and the other probe connected to the DMM on the other conductor. The meter should give a reading approximately equal to the setting on the power supply, if it does not, contact your instructor. 3. Preliminary Measurements In order to find the average electric field, we need to determine the potential difference between the different equipotential lines. Record the positions of both the inner corners of each of the conductors directly onto the second sheet of sheet of graph paper. Place the probe connected to the + side of the DMM (red probe) on the plus conductor and place the probe connected to the minus side (or common) of the DMM (black probe) at a grid point centered on the conductors and located 5 grid lines below the + conductor as indicated in figure 3. Record the potential difference between these two points in the data table below. Move the probe connected to the + lead to where the – probe and move the – probe five grids down. Record the potential difference. Repeat two more times. At the last point, the – probe should be touching the – plate. Figure 2 Data Table for Potential Difference Position of VΩ Probe Position of common Probe ΔV 3. Record Equipotential lines We will record the equipotential lines that we find directly onto the graph paper. Place the probe connected to the + side of the DMM on the grid centered on the conductors and located 5 grid lines below the + conductor as indicated in figure 3. Move the other probe to find 7 positions to each side of the plus probe (a total of 14 ponts) where the potential difference between the two probes is as close to zero as you can find. Record the locations of the + probe and these points on the second sheet of graph paper. Find points that are roughly equally spaced horizontally and include at least three that extend beyond the region between the two conductors on either side. This set of points forms an equipotential surface. Move the + probe 5 grids down and use the same procedure to find another equipotential surface. Again move the + probe 5 grids down and use the same procedure to find another equipotential surface. Figure 3 Location of the + probe for the first set of data + 5 - Data Analysis Data Check It is common for students performing this lab to not have all of the data. Your data should include all of the following. If you are missing any data make sure you obtain it. 1. Spacing per grid on graph paper 2. Potential differences every five grid starting at + plate and ending at – plate 3. Three sets of data for equipotential surfaces with the + probe at 5 grid intervals To analyze your data, connect the data points for the three different equipotential surfaces with a smooth curve. Draw straight lines indicating the positions of the two conductors between the points you recorded for the inside corners. Q7) Describe the shape of the equipotential lines in the interior of the capacitor. Q8) How does the shape of the equipotential lines change in the area exterior to the capacitor? Take the reference of potential to be 0 V on the minus conductor and label each of the equipotential lines (including the conductors) with their respective potentials. Note, you have measured potential differences, not potentials. Q9) Inside the capacitor do the equipotential lines have about the same potential difference between them? If the lines are equally spaced and equidistant, what does this suggest about the electric field in the interior of the capacitor? Your graph should now have 5 equipotential surfaces (remember the two plates are equipotential surfaces) with four regions between the equipotential surfaces. Use equation (1) to find the average field in each of these regions. The correct SI units for the field are V/m but it is quite acceptable and more common use to use units of V/cm to indicate the field strength. Draw a series of arrows on the graph in the correct direction to show the electric field in the interior of the capacitor. Label the arrows with the field strength. Remember the length of the arrows should be proportional to the field strength and the direction should be perpendicular to the equipotential surfaces. Be sure to draw arrows all along the equipotential surfaces to show how the direction changes. Also remember that the field lines point from higher potentials to lower. Q10) What can you conclude about the electric field in the interior of a parallel plate capacitor? Q11) Describe how electric field lines are related to equipotential surfaces.