Lab 2_ElectricField & Pot_updated

Fall 2021 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 calculated using Coulomb’s law. According to Coulomb’s law, Fall 2023 Figure 1: Potential difference between PHYS 2 - Fall 2023

Fall 2021 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 Fall 2023 Figure 2: Schematic showing distribution of PHYS 2 - Fall 2023

Fall 2021 Q.1. How is the potential changing with change in distance? [5 Points] As the distance increases, the potential decreases. There is a decrease in the equipotential as the distance increases . 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) ]. 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] 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 0.2 0.3 0.4 0.5 0.6 Fall 2023 PHYS 2 - Fall 2023

Fall 2021 0.7 0.8 ⮚ 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] Q.2 Describe the direction of the electric field in the region outside the plate. [4 Points] 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] Fall 2023 PHYS 2 - Fall 2023

Fall 2021 Q.1 How are the equipotential surfaces different for the cases of 1,3, and 5 negative charges? [5 Points] Q.2 What do you think is the reason behind these different shapes? [5 Points] 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] Fall 2023 PHYS 2 - Fall 2023

Fall 2021 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? Fall 2023 PHYS 2 - Fall 2023