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E (V/m) 0.5 1 1.5 2 2.5 33 8.99 4.04 2.23 1.42 40 35 30 25 E (V/m) r (m) 20 15 10 5 0 0 0.5 1 y = 8.7x-2.0 1 1.5 r (m) 2 2.5 3 Electric Field Simulation link: https://phet.colorado.edu/en/simulation/charges-and-fields Type “Charges and Fields –PHET” in Google and click the link. Objectives: 1. To understand the magnitude and direction of the electric field produced by a point charge at different directions and distances around the point charge. 2. To understand the magnitude and direction of the electric field produced by a dipole at different directions and distances around the dipole. Before you begin: Your TA has set up a demonstration using two charged electrodes, a pan of water, and an electric field sensor. This sensor has LEDs (light emitting diodes) whose brightness is proportional to the electric field component in the direction that the sensor is pointing. Take a few minutes to move the sensor around and observe how the magnitude and direction of the electric field depends on location. In this lab you will be using a simulation where electric field sensors operate in a similar fashion. 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 𝑄 given by the equation 𝐸 = (4𝜋 ԑ 0 )𝑟 2 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. 1 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. Summarize what you observe about how the direction of the electric field depends on location. 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. E= 4. Predict what the strength of the electric field will be at the same point if you double the amount of charge? E= 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. E= 6. Did your prediction agree? What can you conclude about the dependence of electric field on the amount of charge? 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. r(m) 0.50 1.00 1.50 2.00 2.50 E (N/C) 8. Plot the electric field vs. r graph in Excel. Does your graph show the behavior of the electric field with distance as you predicted in #1, Yes or No? 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 #1, Yes or No? 10. Find the equation of the trend line from Excel and record it below. Also copy your Excel graph into your Word document. Power Law Equation: Now rearrange this equation to be in the same form as the theoretical equation and re-write it in the box. Electric field around a point charge(Theoretical) 𝐸= Electric field around a point charge (experimental) 𝑄 1 4𝜋𝜖0 𝑟 2 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. 𝑘= 1 = 4𝜋𝜖0 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? 3 Part 2: Conclusions 12. 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? Instructions on how to submit the graphs: 1. Open a word document and type the names of all present group members. 2. Copy your Excel graphs (with title and axis labels) to your Word document. 3. Print the document and attach it to the lab write-up. 4

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