Lab 2_ElectricField & Pot_updated

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Fall 2021 Fall 2023 PHYS 2 - Fall 2023 L AB 02 Electric Fields and Potentials Objectives: ● To map electric potential surfaces produced due to differently shaped conductors. ● You will be able to use the relationship between the electric potential and the amount of work done in moving a charge across an equipotential surface to calculate work done on a charge. ● You will be able to trace the electric field lines to plot an equipotential surface. Theory: Two points in an electric field have a difference in electrical potential or voltage if work is required to carry a charge from one point to the other. This work is independent of the path followed between the two points. Consider a simple electric field illustrated in Figure 1. Figure 1: Equipotential Surface Since the charge +Q produces an electric field, a test charge +q at any point in the field will experience a force. It will be necessary to do work to move the test charge between any such points as B and C at different distances from the charge Q . The potential difference between any two points in an electric field is defined as the amount of work done in moving a unit of positive charge between those points. Mathematically, 𝛥𝑉 = 𝑉 2 − 𝑉 1 = −𝑊 𝑞 (1) where Δ V is the potential difference, W is the work done by the electric field, and q is the magnitude of charge moving. If the work W is measured in joules and the charge q in coulomb, then the potential difference Δ V is measured in volts. The amount of force experienced by a charge q 0, placed in the vicinity of another charge Q is calcul ated using Coulomb’s law. According to Coulomb’s law, Figure 1: Potential difference between

Fall 2021 Fall 2023 PHYS 2 - Fall 2023 𝐹 = 𝑘 𝑄 𝑞 𝑜 𝑑 2 (2) where ‘ d’ is the distance between two charges. The conservation of energy principle requires that the work done by the electric field must be independent of the path over which the charge is transported. For example, the amount of energy required to transport a test charge q in Figure 1 from B to C along path ‘a’ should be the same as path ‘b’. If point B in Figure 1 is assumed to be infinitely far away from A , the force experienced by q would be close to zero. The potential difference between C and B (a point at infinity) is called the absolute potential of point C . The absolute potential of a point in an electric field is defined as the amount of work required to move a unit charge from infinity to that point . Mathematically, it is given by 𝑉 = 𝑘𝑄 𝑑 ….. (3) Since both work and charge are scalar quantities, it follows that potential is a scalar quantity. The potential near an isolated positive charge is positive, while that near an isolated negative charge the potential is negative. It is possible to find points around a charge or charge distribution where the value of potential is the same. A surface is drawn that includes all such points is known as an equipotential surface. Figure 2: Electric Field & equipotential surface In Figure 2, the circles around charges A and B are equipotential surfaces. A test charge may be moved along an equipotential line or over an equipotential surface without doing any work. Lines of Force Perpendicular to Equipotential Surfaces: Since no work is done in moving a charge over an equipotential surface it follows that there cannot be any component of the electric field along an equipotential surface. Thus, the electric field (or lines of force) must be perpendicular to the equipotential surface . Equipotential lines or surfaces can be easily located experimentally compared to electric fields, but if either is known the other may be constructed by remembering that the two sets of lines must everywhere be normal to one another. Figure 2: Schematic showing distribution of

Fall 2021 Fall 2023 PHYS 2 - Fall 2023 Lab Work: Go to https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html Spend some time playing/practicing with this simulation. Drag a few positive and negative charges from the bottom and place them on the board. Select the ‘Grid’ option. Drag the ‘Tape’ from the right column to measure the distance between two charges. Use tape to verify that one large grid division = 50 cm and one small grid division = 10 cm. Drag the ‘Voltmeter’ out onto the screen and see how voltage changes when you move closer/farther to a charge. Click on the ‘Pencil’ located on the Voltmeter to draw an equipotential surface! Once you are comfortable with how to use the different buttons , reset the simulation (bottom right circle). Part 1: Characterize the nature of the equipotential surface due to a positive charge ⮚ Uncheck ‘Electric Field’. Select ‘Grid’ and ‘Voltage’. Drag a positive charge an d place it at the center. Remember each charge is 1 𝑛𝐶 =× 10 −9 𝐶 . ⮚ Drag the voltmeter and put it at 10 cm from the charge. Record the value of potential in the Table below. Click on the pencil icon to draw the equipotential surface. ⮚ Complete the table. Use equation 3 for ‘Potential Calculated’. [4 Points] ⮚ Take a screenshot of your equipotential surface and paste it below the table. [4 Points] Distance r (m) 1/Distance 1/r (m -1 ) Potential Measured (V) Potential Calculated (V) 0.1 1/0.1 m -1 83.24 90 V 0.2 1/0.2 m -1 43.44 45 V 0.3 1/0.3 m -1 29.98 30 V 0.4 1/0.4 m -1 22.90 22.5 V 0.5 1/0.5 m -1 18.25 18 V 0.6 1/0.6 m -1 15.18 15 V 0.7 1/0.7 m -1 12.85 12.85

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Fall 2021 Fall 2023 PHYS 2 - Fall 2023 Q.1. How is the potential changing with change in distance? [5 Points] The potential charge decreases with change in distance Q.2 Using Excel draw a graph of 1/r (x-axis) vs. Potential Measured (y-axis). Draw a Scatter Plot and show the best fit line on the graph. Paste your graph below. [6 Points] [The following YouTube video gives you step-by-step instructions on Scatter Plot and drawing Best fit line in Excel https://www.youtube.com/watch?v=xPllgp12uY4 (3:30 min) ]. y = 85.098e -0.293x 0 10 20 30 40 50 60 70 80 90 0 1 2 3 4 5 6 7 8 Distance Vs. Potential Measured

Fall 2021 Fall 2023 PHYS 2 - Fall 2023 Q.3 What is the power of x ? Explain how similar and how different the excel equation is as compared to equation 3. [6 Points] Power of X = -0.293. The equation from the Xcel graph highlights an exponential decrease with increased distance from the charge. Equation 3 just implied that there is a decrease, not necessarily exponential. Part 2: Characterize the equipotential surfaces due to differently charged parallel plates separated by 50 cm ⮚ Reset the Simulation. Uncheck ‘Electric Field’. Select ‘Grid’ and ‘Voltage’. ⮚ Drag positive charges (more than 4) and align those vertically on the screen. Make sure they are tightly fitted, but not overlapping. ⮚ Drag negative charge (same number as the positive charges) and place them 100 cm to the right side of the positive charges. The structure should look like a parallel plate capacitor. ⮚ Drag the voltmeter and put it at 10 cm right of the positive plate. ⮚ Record the value of potential in the Table below. Click on the pencil icon to draw the equipotential surface. Create equipotential surface at 10 cm intervals up to 80 cm. Distance (m) Potential Measured (V) 0.1 160.2 0.2 87.5 0.3 51.91 0.4 24.14 0.5 7.25 0.6 -13.11 0.7 -35.61 0.8 -63.6

Fall 2021 Fall 2023 PHYS 2 - Fall 2023 ⮚ Take a screenshot and paste it below. [4 Points] ⮚ Check the ‘Electric Field’ button. Take a screenshot and paste it below. [4 Points] Q.1 What is the direction of the electric field in between the plates? [4 Points] Toward the negative charge

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Fall 2021 Fall 2023 PHYS 2 - Fall 2023 Q.2 Describe the direction of the electric field in the region outside the plate. [4 Points] It appears to be circling from the positive charge to the negative charge Q.3 Click on the ‘Eraser’ of the voltmeter. This will remove all equipotential surfaces. Now just draw one on each side of the plate at 50 cm. Take a screenshot and paste it below. [5 Points] In the theoretical section, we learned that the electric field is always perpendicular to the equipotential surface. Now, look at the above screenshot and analyze whether the simulation agrees! Write a few sentences on why you agree/disagree. (Just answering Yes/No will not be sufficient to get a full grade). [5 Points] Yes the simulation agrees. At every angle of the arrows the equipotential surface is perpendicular. The bend of the surface line is exactly perpendicular to all electric field arrows. Part 3: Mapping the equipotential surface due to a line and a point charge separated by 50 cm ⮚ Reset the Simulation. Uncheck ‘Electric Field’. Select ‘Grid’ and ‘Voltage’. ⮚ Use a single negative charge and five positive charges to create a distribution as shown in the figure aside. ⮚ Drag the voltmeter and place it at 20 cm to the left of the negative charge. Draw an equipotential surface there and keep moving right by 10 cm until 90 cm. ⮚ Just as above, but to the left of positive charge distribution.

Fall 2021 Fall 2023 PHYS 2 - Fall 2023 ⮚ Take a screenshot and paste it below. [5 Points ⮚ Now add two more negative charges at the same position of the first one so that they are completely overlapping. (In the diagram we should see just one negative charge as two are placed on top of the first one). Repeat the process above to draw equipotential lines and paste the screenshot below. [5 Points] ⮚ Add two more (to make a total of 5) on top (overlapping) and repeat the process to draw equipotential lines and paste screenshot below. [5 Points]

Fall 2021 Fall 2023 PHYS 2 - Fall 2023 Q.1 How are the equipotential surfaces different for the cases of 1,3, and 5 negative charges? [5 Points] In the case of 1, the positive equipotential surfaces completely out-weigh the singular negative charge. As the number of negative charges increase, the equipotential surfaces begin to even out. Q.2 What do you think is the reason behind these different shapes? [5 Points] I believe the difference in shape is due to the placement and orientation of the charges. Part 4: Equipotential lines generated by a multiple charge distribution Create a square as shown in the figure. Q.1 Do equipotential lines intersect? [You are free to draw equipotential lines anywhere you wish. However, you are supposed to write a paragraph based on your equipotential lines to agree or refute the above statement]. [10 Points]

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Fall 2021 Fall 2023 PHYS 2 - Fall 2023 The equipotential surface lines from the simulation do not intersect, so yes, they agree. The different charges and distances have a specific voltage, if the lines were to intersect it would mean that a singular point would have two potentials which is impossible. Electric potential is a property of the sole source charge. The image above reflects this as even when it appears the lines are intersecting, they remain separate. Extra Credit: [You will see similar problem in post-lab] [5 Points] How much work is done in moving a -3μC charge 3 meters from the equipotential surface of 6V to 3V? Work = chagre x (Delta V) (3e-6) x (6-3) = 9 x 10^-6 Joules

Lab 2_ElectricField & Pot_updated

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