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by: Vernie Wehner

Algebra PHYS 2020

Vernie Wehner
GPA 3.88

David Murdock

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David Murdock
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This 10 page Class Notes was uploaded by Vernie Wehner on Wednesday October 21, 2015. The Class Notes belongs to PHYS 2020 at Tennessee Tech University taught by David Murdock in Fall. Since its upload, it has received 33 views. For similar materials see /class/225722/phys-2020-tennessee-tech-university in Physics 2 at Tennessee Tech University.


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Date Created: 10/21/15
Electric Field Mapping 1 Name Electric Field Mapping I Prelimina Questions 1 Give the de nition of Electric Field 2 Give the de nition of Electric Potential 3 How are equipotential lines and electric eld lines related NOTE The next three questions refer to the topographic map you are asked to look up on the web 4 What is the approximate altitude of Rockwell Cemetery 5 If you are at West Cemetery in what direction should you travel if you want to climb most rapidly 6 What is the highest altitude in the Buck Mountain area Your answer should be a range of altitudes within which lies the correct answer Electric Field Mapping 2 Electric Field Mapping Grading III Preliminary Questions 9 points Data Graphs and Tables 12 points Analysis Questions 19 points Objects of the Laboratog To understand how to read and use a contour map To understand the relationship between voltage and electric eld To determine electric elds by measurements of voltage thsical Principles and Description of The concept of an electric eld is related to the observation that electric charges exert forces on other electric charges It is perhaps simpler to introduce the concept of electric eld by rst considering a different eld the gravitational eld You know that if you have an object with mass on earth a force that we call gravity is being exerted on that object We can de ne a quantity called the gravitational eld by considering the force that gravity would exert on a point mass At any point the gravitational eld is the ratio of the gravitational force exerted on the mass to the mass itself a Fmvx g Eg W 1 m It is convenient to talk about the eld even at points where there is no mass to feel the gravitational force This is simple enough to do we just apply equation 1 and understand it to mean the force that would be felt by a mass if it were at that point Near the earth g has a magnitude of approximately 98 ms2 and direction downward An electric field E is de ned in a similar way the difference is that it involves electric force rather than gravitational force and electric charge rather than mass Thus for a point charge q which feels an electric force F MW at a point the electric field at that point is defined to be E E 21mm I 2 9 An important part of the de nition is that the presence of the point charge q often called a test charge must not itself affect other electric charges that are the source of the electric force and thus of the electric eld Most textbooks deal with this issue by adding to the de nition of E that it is the limit of this ratio as q gt 0 Because force is a vector quantity this de nition means that electric eld is also a vector Electric Field Mapping 3 While the electric eld is a crucial aspect of electromagnetism measuring it directly is a dif cult task It is not practical to place an appropriately small charge at many points and measure the forces there It is easier to determine the electric eld by utilizing measurements of the electric potential You have already measured differences in potential numerous times in this semester s labs but you have not made any connection between those measurements and electric elds The connection is made via the work done by the electric force as the test charge moves In the same way that electric eld is de ned as electric force per charge the electric potential is de ned in terms of the work done by that force per charge If the electric force does work W as a test charge moves from point A to point B then the difference in electric potential AVbetween points A and B is de ned as AVE K 3 q Several aspects of the behavior of electric potential can be determined simply from this de nition and from recalling the relationship between work and force 1 If the electric force does positive work as happens when the motion is in the direction of the force then the change in potential is seen to be negative when the test charge is positive Combining this observation with the result from equation 2 that the force and the electric eld have the same direction for a positive test charge you should conclude that the electric potential decreases if you move in the direction of the electric eld 2 In areas of stronger electric field the electric potential will change more rapidly as one moves along the electric eld since a stronger electric eld means a stronger force which in turn means less distance traveled to do the same amount of work 3 For two points to have the same electric potential AV 0 must mean that the work done by the electric force on a test charge moving between those two points must be zero One can ensure that the electric force does zero work by having the test charge always move perpendicular to the electric eld recall that no work is done by a force on an object if the force is always perpendicular to the motion of the object One way to understand the electric eld is to measure the electric potential at many points and map out its behavior Connecting points which have the same electric potential will produce an equipotential line Different equipotential lines are plotted for different values of the electric potential Such a plot often referred to as a contour plot serves the purpose of providing a twodimensional representation of a threedimensional graph 7 the contour lines show the values of electric potential as a function of position coordinates x and y From the argument above the electric eld must always be perpendicular to an equipotential line and it must be in the direction which points toward lower potentials If you do hiking or other outdoor activities you may be familiar with topographic maps Topo maps are used to serve a similar purpose 7 to indicate in two dimensions the Electric Field Mapping 4 value of altitude the third quantity as position changes For an example of a topo map go to the web site httpwwwtop0z0nec0mmapaspz16ampn4003243ampe641116amps25 This shows a topo map of the Buck Mountain area east of Cookeville you should see Buck Mountain printed on the map running nearly vertically The brown lines represent lines of equal altitude you should notice that some of them are bolder and have a number somewhere on them That number represents the height above sea level in feet for instance in the left center of your map you should see such a line labeled 1100 near a marker for Buck Cemetery Lighter brown lines are also contour lines but they will not have numbers on them and you must figure out their altitudes by counting from a bold line On this map you can see that there are 5 divisions between corresponding sets of bold lines so each light brown line must represent a 20foot change in altitude Since the marker for Buck Cemetery is between the 1100 foot dark brown line and the next light brown line on the downhill side you should conclude from this map that Buck Cemetery lies between 1080 and 1100 feet in altitude Now locate the o in the Mountain of the Buck Mountain label Notice that in this area the contour lines are relatively widely spaced However as you move away from this part of the map to either the east right on the map south down or west left you quickly run into a region where the contour lines are much closer together Regions where the contour lines are closer together are steeper since you do not have to travel as far to change altitude by 20 feet 7 these areas must be the sides of the mountain Notice that the quickest way to change altitude is to move perpendicularly to a contour line Now let s return to a discussion of contour maps of electric potential In this lab you will measure values of electric potential at specific values of x y You will then use Excel to create contour plots corresponding to your data Using the fact that electric field lines must cross these contour lines perpendicularly you will then be able to sketch the behavior of the electric field itself If two contour lines are a distance As apart measured perpendicularly and have a difference in potential of AV the magnitude of the electric field is approximately K As E z 4 This approximation becomes more accurate as As becomes smaller and becomes exact in the limit As gt0 In the limit this is of course some type of derivative the complete relation between the vector electric field E and the scalar electric potential can be written in terms of a gradient which should be a topic in Calculus III E V6VfaVj6V 5 6x By 62 To measure voltages in this experiment you will use a digital multimeter A picture of the multimeter is shown in Figure 1 Electric Field Mapping v I MID15 mumquot Figure l A digital multimeter You can use this meter to measure either voltage electric current or resistance by changing the way you connect it and the settings you choose The rotating switch in the center lets you choose not only what quantity you want to measure but also how large a value can be measured on a given setting For this lab you wish to measure DC voltages up to about 25 V39 the DC voltage settings are in the upper right you will see a symbol V with two horizontal lines next to it and you will see settings labeled 200m 2 20 200 1000 alongside the switch Since you need to measure voltages higher than 20 V but less than 200 V you should set this switch to the 200 V setting Connections to this meter are made with a connector called a banana plug that ts snugly into the various connectors along the bottom of the meter To measure voltages you must plug one wire o en referred to as a lead in this context into the port labeled V the far right one and the other into the port labeled COM the port which is second from the right edge A positive reading then means that the voltage lead is at higher potential than the common lead while a negative reading would indicate that the voltage lead is at lower potential than the common lead remember the voltmeter is measuring a difference in voltage between its two leads The COM common port is what is o en called electric ground while the lead from the V port may be called the positive lead Most of the time one chooses ground to be the level of zero electric potential and then just refers to the potential rather than potential difference In this experiment you will use several different metal objects as electrodes when a potential difference is applied to two of these electrodes an electric eld will be created You will use two at electrodes a ring electrode and a point electrode A picture of the materials you will use as electrodes is shown in Figure VI Electric Field Mapping 6 Figure 2 A photograph of the materials used as electrodes in this lab References Fundamentals of Physics Halliday Resnick and Walker John Wiley and Sons Inc Sixth Edition Chapters 23 25 Eguipment Personal computer 25 V Power supply Digital multimeter with two leads Plastic tray Switch Metal ring Metal point electrode 2 pieces aluminum angle iron Transparent ruler 3 wires Warnin s Anytime you are not making measurements open the switch on your circuit to remove the voltage from your electrodes Have your TA or instructor check your circuit before closing the switch or turning on the power supply During the course of the experiment do not touch metal objects such as pipes or plumbing xtures Electric Field Mapping 7 Do not touch any bare metal parts of the circuit while the switch is closed When you are done collecting data turn your power supply off Procedure Begin by opening the le Electric Field Mappingxlt Create a cover page and print a copy for each group member Print a single copy of the worksheets Grid 1 Grid 2 and Grid 3 to use in your measurements Fill your plastic tray with approximately 18 inch of water 7 just enough so that the bottom is completely covered when it s sitting on your lab table Place the copy of Grid 1 under your tray Grid 1 is the grid with the largest squares so that the cross in the center ofthe grid is centered on your tray Take your two pieces of angle iron and place them at the ends of the tray so that they are as far toward the ends of the tray as possible so that they are each parallel to the ends of the tray and so that the vertical part of the angle iron is toward the center of the tray you can see an approximate setup in Figure 3 Figure 3 Photograph showing the positioning of the grid and the two angle iron electrodes What you are going to do is use the power supply to create a potential difference between the two electrodes and then measure the potential at each grid point using the digital multimeter Start by wiring the circuit shown in Figure 4 Electric Field Mapping 8 2222222222 tray probe Figure 4 The power supply is represented here by a battery symbol you should use the connections labeled 0 20 V DC toward the right of the supply The connections to the two angle irons labeled bars in Figure 4 should be made just by clipping a wire to each one The connections for the voltmeter must be made carefully For the positive lead you should use the wire that has a banana plug on one end and a voltage probe a sharp metal tip on the other For the ground lead you should use the wire that has a banana plug on one end and an alligator clip on the other Set up the multimeter to measure voltages up to 200 V DO NOT turn on either your power supply or your multimeter until you have had your circuit checked by your TA or instructor Once your circuit has been approved check that your tray is still centered on the grid and that your angle iron electrodes are at the ends of the tray Turn on the power supply and set the voltage to 25 V DC by adjusting the knob and reading the meter on the supply Turn on your multimeter with the sliding switch on its left side Close the switch in your circuit Touch your voltage probe to one electrode and then the other One should be near 25 V and the other should be near 0 V Analysis Question 1 There are two connections on your power supply for DC operation One is red and one is black Which one corresponds to the higher voltage This is the usual convention for power supplies In order to have Excel make a contour map of the voltages for you you must measure the voltage at every point on a rectangular grid Go to worksheet Sheetl Locate the positive electrode and nd a grid point on your paper that is closest to both the electrode and the side of the tray do not worry about any grid points that do not lie under the tray Place your voltage probe into the water so that the point is directly above the point on the grid and the probe is oriented as vertically as possible Read your voltmeter and record the measurement in cell A1 of your worksheet Move parallel to the electrode to the next grid point measure the voltage and record that reading in cell B1 Continue until you have measured the voltage at each grid point along that line and recorded those values in row 1 of the spreadsheet Then move to the next line in the grid parallel to the electrode start at the same side of the tray as you did earlier and measure at each grid point record these measurements in row 2 Move to the next line and record those measurements in row 3 Continue in a similar fashion until Electric Field Mapping 9 your worksheet contains values measured at every grid point which is inside the edges of the tray Open the switch to remove electric bias from the electrodes Now you are ready to create the contour plot Follow these instructions 1 Select the rectangular area containing your data Do not include any empty cells 2 Start the Chart Wizard by choosing the icon that looks like a bar graph in red yellow and blue Under Chart Type choose Surface Under Chart subtype choose 3D Surface in the lower left of the four options 5 Choose Next to advance to Step 2 of the Chart Wizard 6 Choose Next to advance to Step 3 of the Chart Wizard Enter a title for you graph Choose Next to advance to Step 4 of the Chart Wizard 8 Choose As new sheet for the placement of the graph and choose Finish 5 gt1 You should now have a contour plot of your voltage measurements on the screen It will look somewhat different from the topo map because Excel colors in each region between contour lines with different colors at this point you should have five different regions on your graph The equipotential lines are the lines separating one color from an adjacent color At the right edge of your graph is the legend which tells you the voltage range to which each color corresponds The horizontal axis of the graph will be labeled with integers which identify the row in the spreadsheet the vertical axis is labeled on the right with S1 S2 corresponding to various columns in the spreadsheet Thus for example the position corresponding to a horizontal axis label of 4 and vertical axis label of S2 has the value in cell B4 4Lh row 2quotd column of your spreadsheet By default Excel creates these plots with five different regions because your voltages in this case are in the range 0 7 25 V each of these regions has a range of 5 V These are shown on the graph s legend However often you can see more details if you have more equipotential lines You can change the spacing of equipotential lines by the following procedure 1 Rightclick on the legend and choose Format Legend 2 Choose the Scale tab 3 Change the value in Major Unit it will be 5 when you get there Start by entering 3 in this box 4 Choose OK Analysis Question 2 How did your graph change when you changed the spacing between equipotential lines Which of these two graphs do you prefer and why Try some other values for the spacing between equipotential lines Try values larger than 5 and smaller than 1 to be sure you have a good feel for how this change affects your graph While there is no right or wrong choice here one issue that we have to contend with is that Excel depends on color to help distinguish regions However your printer is not a color Electric Field Mapping 10 printer and if there are too many colors it can be difficult to distinguish different regions on a printed copy We recommend that for this graph you choose an interval between contour lines that is somewhere around 2 V Once you settle on a final graph print a copy for each group member Analysis Question 3 Describe the behavior of the equipotential lines that you observe What does this tell you about the direction of the electric field at different points between the electrodes Analysis Question 4 Remove the grid from beneath your tray and use your ruler to determine the size of the grids Combine this with information from your graph to estimate the magnitude of the electric field near the center of the tray Analysis Question 5 Using your graph of equipotential lines and the relationship between voltage and electric field state how the electric field varies as you move among different points between the electrodes Next you will measure voltage in a different situation Take your copy of Grid 2 the middlesized grid and center it under your tray Check to make sure that the electrodes are all the way against the ends Take the metal ring and place it in the tray so that it is centered on the cross on your grid Once everything is in place close the switch Once again make measurements at each grid point inside the edges of the tray If a grid point lies underneath the ring get your probe as close to it as you can WITHOUT MOVING THE RING Record your values on worksheet Sheet2 Once you have all the points measured open the switch and turn off the power supply Generate a surface plot for these voltage measurements Adjust the interval between equipotential lines to 15 V and print a copy of the graph for each group member Sketch the approximate position of the ring on each graph Analysis Question 6 Starting at the positive electrode and ending at the negative ground electrode sketch at least three electric field lines Remember that electric field lines must always be perpendicular to equipotential lines including equipotential lines that may not be shown on your plot Analysis Question 7 Describe how the presence of the ring changes the electric field not the potential Analysis Question 8 How does the magnitude of the electric field inside the ring compare to the magnitude outside the ring Include an explanation of how you reached this conclusion Analysis Question 9 What do your data say about the direction of the electric field just outside the ring Next take Grid 3 and center it under your tray this grid will not extend under the entire tray Remove the electrodes from the tray place them on the paper towels provided and center your ring on the grid Wire the circuit shown in Figure 5


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