Lab2-The Electric Field

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Dec 6, 2023

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The Electric Field NAME: _____Sehajpartap Gill___________________ Date: ____7/16/2021_______ Lab Partner’s: ____________________________________________ Access the University of Colorado’s PhET simulation: Charges and Fields Objectives:  To understand the magnitude and direction of the electric field produced by a point charge at different directions and distances around the point charge.  To understand the magnitude and direction of the electric field produced by a dipole at different directions and distances around the dipole. INSTRUCTIONS: Use Excel to plot the graphs and insert or attach all graphs, plots, and tables to this lab assignment. Convert values to SI units and show all your calculations. Part 1: Electric Field from One Point Charge 1.) The strength of the electric field around a positive point charge Q at a distance r from the center of the charge is E = k Q r 2 ; k = 1 4 π ϵ 0 The direction of the electric field vector is radially outward. Sketch a E vs. r graph for a positive charge. Label the horizontal and vertical axes of the graph. 1

2.) Now open the simulation. Activate “Grid” and “Values”. Place a 1 nC positive (red color) charge on the grid. This is sometimes called a source charge since it’s the source of the electric field we are going to measure. To make a measurement of electric field, grab an E- field sensor (yellow dot) and place it where you want to measure the electric field. The arrow of the sensor indicates the direction of the E-field at that point and the length of the arrow is proportional to the strength of the electric field. Move the sensor around and observe how the electric field is different in magnitude and direction at different locations. Summarize what you observe about how the magnitude of the electric depends on location. If we double the distance the field of strength with ¼th of its original, the magnitude of the electric field is inversely proportional to the square of the distance between the original and the original location. Summarize what you observe about how the direction of the electric field depends on location. The direction of the E field will be pointing away from the origin (because the charge is positive) along the line joining the location and origin. 3.) Make a measurement of the electric field 1.0 m away from the charge (scale is shown at bottom of the screen, or you can use the measuring tape on the right). Note that the units of electric field are V/m = N/C. Record the value. E = ¿ _____ 9 N/C____________ 4.) Predict what the strength of the electric field will be at the same point if you double the amount of charge. E = ¿ _____ 18 N/C____________ 5.) Place another 1 nC positive charge on top of the previous charge and again measure the electric field at the same place. Record your result and put back the added charge in the charge bucket. E = ¿ _____ 27 N/C____________ 6.) Did your prediction agree? What can you conclude about the dependence of electric field on the amount of charge? Explain . Yes, my prediction agrees, as we can see from equation, electric field is directly proportional to the source charge. More the charge, more will be the electric field at given distance. 2

7.) Now we want to investigate how the strength of the electric field depends on distance from the 1 nC positive charge. Make measurements of the magnitude of the electric field at different r values and complete the following table, where r is the distance measured in meters. 8.) Open Excel and Plot the E vs. r graph. Does your graph show the behavior of the electric field with distance as you predicted in problem 1? Explain . 0.5 1 1.5 2 2.5 0 5 10 15 20 25 30 35 40 Electric Field Vs Distance Distance Electric Field 9.) Select a Power Law trend line to fit the data and display the equation. Does your power law fitting give the same dependence of the electric field with distance as you described in problem 1? Explain . Yes, even with the power law trend line fit on the graph, it gives the same dependence of th electric field with the distance as predicted. 10.) Find the equation of the trend line and record it below. Power Law Equation : ___Y = 4.3403x^-2.09 ___________ 3 r (m) E (N/C) 0.5 36 1 9 1.5 4 2 2.25 2.5 1.44

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Now rearrange this equation to be in the same form as the theoretical equation and re- write it in the box below. Compare the equation you obtained with the theoretical equation of electric field around a point charge. From your comparison calculate your experimental determination of the electrostatic constant, k . ( Hint : Note that the coefficient of the power law equation is kQ .) Show calculations to find k and % error. k = 1 4 π ϵ 0 = ¿ 11.) Remove the positive charge and place a 1 nC negative (blue color) charge at the same place. What is different and what is the same about the electric field due to 1 nC negative charge compared with 1 nC positive electric charge? Explain. The Electric field due to a point charge follows the inverse square law that we see as: However, if we replace the 1nC positive charge by a 1nC negative charge the magnitude of the electric field at any point will be same as that of due to positive charge but the direction of the electric field will be changed. In case of positive charge, the electric field is outward direction (the field line should be coming out of the charge) while in case of negative charge the field is inward direction (the field line should be going inward to the charge. 4 Electric field around a point charge (theoretical) Electric field around a point charge (empirical) E = 4.3403/ r^2.09

Part 2: Electric Field from an Electric Dipole Since atoms in a molecule often carry a net charge, many molecules are permanent electric dipoles. The figures below show a carbon monoxide molecule, CO, and a water molecule, H 2 O, characterized by the dipole moment with a magnitude of ? = 𝑞? , where q is the charge and ? is the distance between the charges. The direction of the dipole moment is defined from negative charge to positive, as shown. The units of dipole moment are units of charge multiplied by units of distance, such as a Cm. 12.) Now we will examine the electric field of a dipole. The magnitude and direction of the electric field depend on the distance and the direction. We will investigate in detail just two directions. With the charges available in the simulation how do you create a dipole with dipole moment 1 x 10 -9 Cm with a direction for the dipole moment pointing to the right? Look back at the figure above to make sure you determined the direction of the dipole moment correctly. Make a sketch in the next box that shows the amounts of charge and the distance between the charges. There are many correct answers. 5

13.) On your drawing in problem 12, mark the center of the dipole as the origin ( x =0, y =0). Pick a point to the right of the charges and mark it as P 1 . At that point draw vectors to represent the electric field contributions from each of the individual charges in your dipole. Each electric field vector should be drawn with its tail at point P 1 . Also draw a vector to represent the net electric field produced by both charges in the dipole. Label that vectors E net 14.) Now reproduce the dipole on the grid in the simulation making sure that the dipole moment is directed to the right and the magnitude of the dipole moment is 1 x 10 -9 Cm. Make the center of the dipole to be the origin ( x =0 m, y =0 m) on the grid. 6

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15.) Make measurements of ? at a series of points along the x-axis to the right of the dipole and record its magnitude and direction at each position. 16.) Use Excel to Plot the measured dipole electric field strength vs. r graph. Which electric field (single charge or dipole) drops off more with distance? Use the electric field graphs to support and explain your answer. 1 1.5 2 2.5 3 0 2 4 6 8 10 12 14 16 18 20 Electric Field Vs Distane Distance Electric Field 17.) Make some measurements of ? at points along the x -axis to the left of the dipole. How do the magnitude and direction of the electric field on the left side of the dipole compared to the right side for the same distance? 7 x (m) y (m) E (N/C) Direction 1 0 18.02 To the right 1.5 0 5.33 To the right 2 0 2.25 To the right 2.5 0 1.152 To the right 3 0 .667 To the right

18.) On your drawing in problem 12, pick a point above the center of the dipole and mark it as P 2 . At that point draw vectors to represent the electric field contributions from each of the individual charges in your dipole. Each electric field vector should be drawn with its tail at point P 2 . Also draw a vector to represent the net electric field produced by both charges in the dipole. Label that vector as E net 19.) Make measurements of ? at a series of points along the y -axis above the dipole and record its magnitude and direction at each position. 20.) Make some measurements of ? at points along the y -axis below the dipole. How do the magnitude and direction of the electric field above the dipole compare to below the dipole? 8 x (m) y (m) E (N/C) Direction 0 0.5 72 To the left 0 1.0 9 To the left 0 1.5 2.67 To the left 0 2.0 1.125 To the left 0 2.5 .576 To the left

QUERIES: 21.) Summarize what you observed about the magnitude and direction of the electric field from a single point charge. How does the electric field depend on distance from the point charge? As we have discussed above the electric field follows the inverse square law. It means if we move away from the charge, it’s magnitude of the electric field will decrease according to square of distance from the given charge. The nature of the field depends on what type of charge we have given. 22.) Summarize what you observed about the magnitude and direction of the electric field from a dipole. In particular, how does it depend on distance and direction from the center of the dipole? The electric field due an electric dipole follows the inverse cube law means the electric field due to a dipole varies as inverse of cube of the distance from the center of the electric dipole. if we move away from the electric dipole the magnitude of the electric field also decreases but with cube of the distance from the center of the electric dipole unlikely as in case of a point charge it follows the inverse square law. CONCLUSION In conclusion to this experiment, we know that a single point charge follows the inverse square law, meaning if it moves away from the charge, its magnitude of the electric field will decrease depending on the square of the distance; if it’s a dipole charge (electric dipole), it follows the inverse cube law and the magnitude of this will also decrease but according to the cube of the distance as it moves away for the electric dipole. Replacing 1nC positive charge by a 1Nc negative charge results in the same magnitude of the electric field at any point because of the positive charge, however the direction of the electric field will change. Positive charges have a outward direction for the electric field and negative charges inward. 9

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Lab2-The Electric Field

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