Lab 2_Electric Field Lines-1

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Apr 3, 2024

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1 LAB 2: ELECTRIC FIELD LINES Date Lead Author Lead Experimentalist Associate Experimentalist Objective: Qualitative study of electric fields. Purpose: To better understand the relationship between equipotentials and electric fields. Introduction The magnitude of an electric field in the space surrounding a source charge is written as |? ⃗ | = 𝑘 𝑒 |𝑄| ? 2 = | ? ? | where E has units of Newtons per Coulomb (N/C). The electric field represents the electric force per unit charge and is shown by the field lines that start on positive charges and end on negative charges. The direction of these lines indicates the direction of the force would act on a positive test charge placed along the line. Note that field lines are continuous, smooth curves and should not be confused with field vectors, which are used to show the field at discrete points. Electric field lines are tangent to electric field vectors. The electric potential of a point charge is given by 𝑉 = 𝑘 𝑒 ? ? Figure 1: Representation of electric field lines (blue solid lines) and equipotential lines (gray dash lines) where V has units of Nm/C = Volts (V). Near charged objects we can find equipotential surfaces on which the electric potential is the same everywhere. For a point charge, the equipotential surfaces are spheres centered on the charge. We represent these in 2-D as circles. The dashed lines in the figure below illustrate the scaling of voltage at equal increments- the equipotential lines get further apart with increasing distance. Electric field lines are always perpendicular to equipotential surfaces, as illustrated in the Figure 1.

2 Experiment The purpose of this lab is to draw the electric field lines and equipotential surfaces for several different charge configurations. A computer program will be used to help you visualize these qualities. When drawing your diagrams, remember that too many lines can sometimes make the diagram confusing, whereas too few lines may not sufficiently show the pattern. Part 1: Electric field lines  Open the simulator at https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html • Charges can be added or removed by clicking on a charge and dragging it into the open area or back into the supply. To increase the charge magnitude, place multiple charges on top of each other. 1. Draw the electric field lines for each of the different charge configurations shown in Fig 2. To do this, position the charges in the simulation and then click on the ”Electric Field” option to display the electric field vectors. Determine the shape of the electric field lines by noting that they are tangent to the field vectors shown in the simulation. Remember that your field lines need to start on charges and end on another charge or at the edge of the box. [10 pts] 2. Next, draw the equipotential surfaces for the charge configuration by using the blue “Equipo - tential Finder.” Move the finder by clicking in the center of the box and dragging it to the location where you would like to have an equipotential line drawn. Click the pencil icon and an equipotential line that intersects the bulls-eye on top of the box will be drawn. Draw at least TEN additional lines by clicking in different areas. Remember that equipotential surfaces are lines that indicate a constant electric potential around a charge configuration (analogous to lines on a topography map that indicate constant altitude). [10 pts] 3. Looking at the electric field lines you drew, find a location on one figure where you expect the electric field to be equal to zero. Re-create that charge configuration in the simulation and use the electric field sensor (yellow dot in the box next to the charges) to confirm your prediction. Draw a star on the figure at this location. Hint at this location the electric field vectors due to each charge must cancel. There should be no field lines present at such a location. [5 pts] 4. Now look at the equipotential surfaces you drew. Find a location on one figure where you expect the electric potential to be equal to zero. Re-create that charge configuration in the simulation and use the Equipotential Finder to confirm your prediction by placing the crosshair at that spot and reading the potential. Draw a triangle on the figure at this location. Hint at this location the potential values due to each charge must cancel. The sign of the electric potential is determined by the sign of the charge creating it. [5 pts]

3 Fig. 2: Three different charge configurations. For each, you will draw the electric field lines (left side) and the equipotential surfaces (right side) by using the computer simulation.

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4 Part 2: Electric field hockey • Open the “Electric Field Hockey.” simulator at https://phet.colorado.edu/sims/cheerpj/electric- hockey/latest/electric-hockey.html?simulation=electric-hockey • You can add positive or negative charges to the playing field from the boxes on the top right of the window. Leave the puck positive but change the mass to 50. It is also helpful to enable the “Trace” and “Field” boxes, as these will allow you to visualize the field l ines as well as the resulting path of your particle. • Feel free to spend some time on the practice level, getting used to the way the particle moves with different charges on the field. When you are ready, change to difficulty level 1 and attempt to move the particle into the goal. 5. When you have found a charge configuration that is successful, sketch the location of the charges used as well as the resulting path of the particle in Fig. 3 . Fig. 3: Draw the configuration of charges used to beat level 1 of Electric Field Hockey, as well as the path taken by the particle. [15 pts] 6. The electric field can be expressed in units of either N/C or V/m. Show that these two units are equivalent. Hint - rewrite V/m in more fundamental units. [10 pts]

5 Application Question 7. Two point charges are fixed on the x-axis. Each has a positive charge q . One is at x = − a and the other is at x = +a. Draw the field lines and equipotential surfaces on the figure below. Write expressions for the electric field and electric potential at the origin and explain your results? [15 pts]

6 Results and Conclusions (20 pts) Briefly summarize the objective of today’s lab as well as the results of your experiment. State any applicable errors you calculated and give AT LEAST two possible reasons your results deviated from theoretical values. If the experiment was purely qualitative (i.e. you did not calculate a % difference or % error), you may replace the two sources of error with two SPECIFIC concepts from lecture that the experiment demonstrated. Objective: The objective of today’s lab was to observe using the method of Results: We observed and this DID / DID NOT agree with our expectations at the beginning of the experiment because Concepts from lecture: We observed the following two concepts from lecture 1. 2. and they related to this lab because

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