The Electric Field Simulation Laboratory

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Tarrant County College, Fort Worth *

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1201

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Physics

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Feb 20, 2024

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The Electric Field 1 NAME:__________________________________ DATE: __________________________________ Access the University of Colorado’s PhET Charges & Fields simulation at https://phet.colorado.edu/en/simulation/charges-and-fields (Type “Charges and Fields –PHET” in Google and click the link) 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. 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 𝐸𝐸 = 𝑘𝑘 𝑄𝑄 𝑟𝑟 2 ; 𝑘𝑘 = 1 4𝜋𝜋𝜖𝜖 0 The direction of the electric field vector is radially outward. Sketch E vs. r graph for a positive charge. Label the horizontal and vertical axes of the graph.

2 2.) Now open the simulation. Activate “grid” and “show numbers” to read 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 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 below. Summarize what you observe about how the direction of the electric field depends on location below. 3.) Make a measurement of the electric field at 1.0 m away from the charge (scale is shown at bottom of the screen). Note that the units of electric field are V/m = N/C . Record the value below. 𝐸𝐸 = _________________ 4.) Predict what the strength of the electric field will be at the same point if you double the amount of charge? 𝐸𝐸 = _________________ 5.) Place another 1 nC positive charge on top of the previous charge and measure the electric field again at the same place. Record your result below and put back the added charge in the charge bucket. 𝐸𝐸 = _________________ 6.) Did your prediction agree? What can you conclude about the dependence of electric field on the amount of charge?

3 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.) Plot the E vs. r graph. Does your graph show the behavior of the electric field with distance as you predicted in problem 1? 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? 10.) Find the equation of the trend line from a graphing application (Excel) and record it below. Power Law Equation : ___________________________________ 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 point charge. From your comparison calculate your experimental determination of the electrostatic constant, k . 𝑘𝑘 = 1 4 𝜋𝜋𝜖𝜖 0 = r(m) E (N/C) 0.5 1 1.5 2 2.5 Electric field around a point charge (theoretical) Electric field around a point charge (empirical)

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4 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? 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 shows a carbon monoxide molecule, CO , and a water molecule, H 2 O dipole is characterized by the dipole moment with a magnitude of 𝑝𝑝 = 𝑞𝑞𝑞𝑞 , where q is the charge and 𝑞𝑞 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 depends on the distance and the direction. We will investigate in detail just two directions. With charges available in the simulation how do you create a dipole with dipole moment 1 x 10 -9 C-m with a direction for the dipole moment pointing to the right? Look back at the figure at the top of the page to make sure you determined the direction of the dipole moment correctly. Make a sketch below 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 above, 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 all the charges in the dipole. Label that vector 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. 15.) Make measurements of 𝐸𝐸 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.) 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. 17.) Make some measurements of 𝐸𝐸 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 compare to the right side for the same distance? x (m) y (m) E (N/C) Direction 1 0 1.5 0 2 0 2.5 0 3 0

6 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 all the charges in the dipole. Label that vector as E net 19.) Make measurements of 𝐸𝐸 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 𝐸𝐸 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? x (m) y (m) E (N/C) Direction 0 0.5 0 1.0 0 1.5 0 2.0 0 2.5

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7 Part 3: Conclusions & Queries 21.) Summarize what you observed about the magnitude and direction of the electric field from a single point charge. In particular, how does the electric field depend on distance from the point charge? 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?

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