Mini-lab: Equipotential Lines and Gradients
Purpose: We will measure equipotential lines on a sheet and determine the electric field patterns through the use of the gradient concept.
Procedure: Hook up two cables from a power supply to one of the conductive sheets. Turn up the voltage in order to set up a potential difference between the two ends of the sheet.
Using a multimeter, measure the voltage going down the center of the sheet from one end to the other at 2 or 3 cm intervals.
Now try to measure equipotential lines going side to side. You may want to find the lines every 0.25 volts apart, for instance. Draw these lines on a clean sheet of white recording paper in pencil, and once you have a pattern draw in the electric field lines in ink, indicating the direction of the E-field.
Observations and Questions:
1. In words, what does E = -dV/dr mean physically. Some find it easier to think of this more generically as E = -DV / Dr, instead. Indicate the significance of the minus sign.
2. On your sheet, include arrows showing which way the electric field vectors are directed. To do this you will have to determine which end of your sheet is at a higher potential, and which is at a lower potential. Use measurements from the multimeter to determine this.
3. Why can an electric field vector not run parallel to an equipotential line?
4. How can you tell on your ‘map’ where the electric field is strongest? Weakest? Explain your reasoning.
5. Pick two equipotential lines on your map. Using the voltage values you measured and distance measurements, determine the approximate strength of the electric field between those two lines.
6. How much work would be done if you moved an electron from one of the equipotential lines used in #5 to the second equipotential line? The charge of an electron is 1.6 x 10-19 C. Also, what is the maximum speed an electron and proton could attain if energized by that voltage? The mass of an electron is
9.1 x 10-31 kg, and that of a proton is 1.6 x 10-27 kg.
7. In problems like #6, what determines if positive work is done by the electric field? Give your answer both in words and with a mathematical argument.
8. I’d like you to work your way through the ActivPhysics simulation 11.11, Electric Potential: Qualitative Introduction lesson (11.11). Try the simulations with the questions being asked; I’ll be looking for feedback from you about whether you think this is helpful or not.
When done with your lab, do the 1986 AP problem with equipotential lines.