Electric Field Mapping

Introduction

Charges create electric fields and electric fields apply forces to charges. The concept of electric fields is very similar to gravitational fields, yet often much harder for students to understand. Use this demonstration to map the electric field created by various types of conductors.

Concepts

• Electric fields
• Equipotential lines
• Electric potential
• Coulomb’s law

Background

The fundamental principle of electrostatics is that like charges repel, and opposite charges attract. Students often compare charges to magnetic poles in terms of attraction and repulsion. Electricity and magnetism are interrelated but, interestingly, an analogy can also be drawn between electricity and gravity. Gravity and electrostatics are similar in many ways. Both have basic unit particles—mass for gravity and charge for electrostatics—and both exert a force on similar particles of mass or charge. The attractive force between two masses is described by the following equation, known as Newton’s law:

where

G = Gravitational constant
m = mass
r = distance between the two masses

The force between two charges is considered repulsive when positive and attractive when negative, and is shown by the equation known as Coulomb’s law: where

k = Coulomb’s constant
q = charge
r = distance between the charges

Both the gravitational and electrostatic forces obey an inverse square law—as objects get further apart, the force between them drops by the inverse square of the distance.

Electric fields were first proposed by the British scientist Michael Faraday (1791–1867). He used the concept of an electric field to show how two charged bodies can affect each other without touching, and without any medium to transport the energy. Faraday demonstrated the existence of an electric field by showing the effect a charged object would have upon a small test charge. A test charge is used as a concept, and not an actual physical reality, to understand what effect the conductors have on their space; if an actual charge were placed in the electric field, it would affect its surroundings and likewise exert a force on the surrounding charges. The electric field is the force per unit charge at a given point in space. It is shown by the equation where

E = electric field at the location of a test charge
F = force on the test charge
q = positive test charge

Direction is important when it comes to electric fields. By convention, electric fields are defined as the force on a positive test charge. An electric field would emanate away from a positive charge, and point inward towards a negative charge (see Figures 1 and 2). The gravitational field–electric field analogy can be extended further using the concept of high and low ground. Positive charge corresponds with “high” ground, negative charge corresponds with “low” ground, where objects or charges will tend to move. Work done on an object, such as a ball, to bring it up a hill will increase its potential energy. Likewise, there is potential energy stored in electric fields—a positive test charge placed near another positive charge will experience a greater force than one that is far away. When released, a positive test charge will accelerate away from the positive charge and towards the negative one, and just like a ball rolling down a hill, will turn its potential energy into kinetic energy. The potential energy in electric fields is most often expressed in terms of the difference between two points. The unit for electric potential difference, the volt (V), is defined as the potential difference between two points that would require one joule (J) of external work to move one coulomb (C) of charge from one point to the other (Equation 4). Understanding electric potential difference is important because electric fields are difficult to measure directly. Because an electric field is defined as the force on a charge, if the charge were free to move, it would follow the direction of force. This direction can be found by considering the direction of the greatest potential energy change—in other words, by measuring the voltage using a voltmeter. In this demonstration, conductive paper and silver ink will be used to create a variety of charge configurations. The conductive paper is layered with carbon, which is conductive, but not nearly as conductive as the silver ink. This ensures the resistance between the two points is uniform, making the paper behave like an insulator, while at the same time creating a complete circuit with the electrodes, making it possible to measure the voltage at all points. Since voltage is always measured with respect to an arbitrary ground, two types of measurements can be made here—the electric field lines, which correspond to the direction of greatest change, from point to point, and the equipotential lines. Equipotential lines are lines where the potential energy is equal, and are measured with respect to an electrode. An analogy for equipotential lines, which follow the direction of no change, is a ball rolling around a hill while staying at the same height (see Figure 3). A charged particle following an equipotential line would experience no change in potential energy. In this demonstration, it will be much quicker and easier to map the equipotential lines first. Since the equipotential lines correspond to the lines of no change in potential energy, the lines of the greatest change in potential energy must always be perpendicular at the intersection. In Part A, you will map the equipotential field lines and then draw in the electric field lines perpendicular to them (see Figure 6 in the Procedure section). Part B, which is optional, gives the procedure for mapping the electric field lines. This second procedure is fairly lengthy—it might be best to map only one electric field line and compare it to the estimated line for demonstration purposes.

Materials

Safety Precautions

Silver conductive ink is flammable; keep cap tightly closed and away from all sources if ignition. Avoid contact with skin and eyes as it may cause irritation. Slightly toxic on inhalation; ensure adequate ventilation when using. Wear safety glasses and gloves when using. Aluminum pushpins are sharp and may prick fingers. Wash hands thoroughly with soap and water before leaving the laboratory. Follow all laboratory safety guidelines.

Disposal

The silver conductive pen should last about one year if the pen is capped and stored properly. It may be discarded when dry. The conductive sheets may be saved and stored for future use.

Prelab Preparation

1. Make enough copies of the Electric Field Plotting Map for each student to graph the multiple configurations that will be tested (template provided in Teacher PDF).
2. Practice the electrode configuration you plan to use by sketching it out on the graphing paper provided. Note: A point charge configuration, a conducting plates configuration, and a conductive obstacle configuration are recommended. Electrode configuration suggestions can be found in Teacher PDF.
3. Tap the top of the conductive pen on a hard surface to free the mixing balls, then shake vigorously for 20 seconds to mix the ink.
4. Practice using the pen on the sketch by squeezing the barrel firmly and drawing a small line. Note: A great deal of pressure is sometimes required to start the silver ink flowing, but be careful not to over squeeze, lest the top pops off. If necessary, fold the pen between your hands and press together using your palms firmly and evenly.
5. When ready, draw out the shapes on the conductive paper. Note: Be careful not to press too hard! The paper can get scratched easily. Scratched paper can still be used to give good results, but the data may be less reliable.
6. The ink should reach optimal conductivity by 45 minutes, although it will begin to be conductive within 5–10 minutes. Set paper aside to dry where it will not be disturbed.
7. Repeat the process to make as many “electrode maps” as desired.
8. (Optional) This demonstration may be easiest to show students through use of an overhead projector. Copy the Electric Field Plotting Map (see attached) onto a transparency sheet and use a transparent voltmeter (Flinn Catalog No. AP5668).

Procedure

Part A. Equipotential Line Mapping

1. Attach the conductive paper with the silver “electrode map” to the cardboard sheet using plastic pushpins, one pin into each corner, and insert a cork (see Figure 4).
   {12749_Procedure_Figure_4}
2. Using the aluminum pushpins, push one into each point on the silver conductor shapes—the pins will be the electrodes. Note: Do not push the pins all the way down into point charges, as the pin heads will cover the silver point charges. Instead, push in just enough to make electrical contact between the silver ink and the aluminum electrode (see Figure 4).
3. (Optional) Place the transparency and projection voltmeter on an overhead projector or draw a rough outline of the graph on the board.
4. Attach one alligator lead from each pushpin electrode to the positive or ground (or “negative”) terminals of the power supply or battery. Set the power supply to 6 volts (see Figure 5). Note: When working with batteries, it is important to disconnect the wires when not in use, so as not to waste the battery or overheat the wires.
   {12749_Procedure_Figure_5}
5. Using a voltmeter, hold the ground lead to the negative silver electrode on the field map. Note: Do not ground on the aluminum pins, as this will affect the results.
6. Using the positive lead of the voltmeter, slowly and carefully drag the lead across the conductive paper away from the electrode until the voltmeter reads 1 volt. Note: Be very careful dragging the leads, and do not scratch the conductive paper!
7. Mark this point on the board or transparency, and have students record the point in their Electric Field Plotting Maps.
8. Keeping the negative voltmeter lead on the negative electrode, repeat step 5 towards a new point many times, marking each point on the map.
9. Repeat step 8 several times. Draw a best-fit line connecting the 1-V marks (see Figure 6).
   {12749_Procedure_Figure_6}
10. Repeat steps 6–9 to map 2-V, 3-V, 4-V and 5-V marks. Note that any voltage difference may be chosen (.5-V, 2-V, etc.), as long as it is kept constant.
11. Disconnect the battery or power supply.
12. On the board or transparency, draw a rough sketch of a few electric field lines. Start at the electrode and point towards one of the equipotential lines, in order to intersect it at a right angle. Continue to trace this across the sheet, filling in multiple lines (see Figure 6).

Part B. Electric Field Mapping (Optional)

13. Using a small object such as a nut or pen cap, space the voltmeter leads 3–4 cm apart, and tape them together at this distance (see Figure 7).
    {12749_Procedure_Figure_7}
14. Connect the battery or turn on the power supply and set it to 6 V.
15. Using the negative lead as the ground lead, choose a spot near the positive electrode on the conductive paper. Do not ground the lead on the electrode itself. Lightly brush the positive test lead against the conductive paper in a hemisphere (similar to drawing with a compass) to find the greatest voltage.
16. Mark the location and voltage on the board or transparency. Have students record the data on the Electric Field Plotting Map.
17. Put the negative test lead at this new point as the ground. Once again, lightly brush the positive test lead in a hemisphere, finding the greatest voltage. Mark this location and voltage on the overhead, and set it again as the new ground.
18. Repeat step 14, always carrying the line in the direction of the greatest voltage change, until the negative electrode on the conductive paper is reached.
19. To start a new line, pick a new spot near the positive electrode and ground the negative test lead there. Repeat steps 15–18.

 

Student Worksheet PDF

12749_Student1.pdf

12749_Teacher1.pdf

Teacher Tips

• Kit contains enough materials to test 10 different electrode configurations. All components are reusable.
• This demonstration fits into the electrostatics portion of a physical science curriculum. It would also work well as an activity stations lab. Set up each student group with a single electrode configuration and have students rotate as time permits.
• It may be difficult to get ink to start flowing out of the pen, due to the settling of silver particles. Shake the pen well and apply a great deal of pressure to the pen barrel.
• In the case of optional electric field mapping (Part B), using a higher voltage than 6 V may make the measurement process easier. (A higher voltage difference will make it easier to pinpoint the highest volt reading.) Likewise, the further apart the two voltmeter leads are taped, the greater potential energy difference will result. The tradeoff in the case of the latter is less distinct field lines.
• Use a projection voltmeter (available from Flinn Scientific, Catalog No. AP5688) to display the readings on a projector allowing students to see the measurements themselves.
• Experiment with insulators by cutting out shapes from the conductive paper. The absence of conducting materials will demonstrate the nonconducting properties of insulators and their effects on electric fields.
• If a cardboard sheet is not available, the bottom of the kit box makes a handy sheet. Simply turn the box upside down and attach the conductive paper using the pushpins.

Sample Data

Sketch the equipotential lines for each of the conductor arrangements demonstrated by your teacher. Fill in additional lines based on the observed pattern. Then fill in the electric field lines based on your teacher’s instructions.

Student answers will vary

Answers to Questions

Point Charges

1. Where is the field mostly uniform, showing lines most evenly spaced? Why might this be so?

   The field is mostly uniform nearest the two point charges, where the individual charge has a greater effect than charges farther away.

2. The two electrodes tested were opposite charges. Sketch your best guess for the field lines of two same-charge point electrodes.

   Student answers will vary (see Figure 8).

   {12749_Answers_Figure_8}

Parallel Plates

3. Describe the electric field between the parallel plates.

   The electric field between the plates is uniform, with straight lines pointing directly to the other plate.

4. What happens to the field lines and equipotential lines near the top and bottom edges of the plate?

   The field begins to get warped near the edges of the plate, and is no longer uniform. In the same way, the equipotential lines begin to curve, instead of staying straight.

Synthesis Questions

5. Why must the electric field lines and the equipotential lines be perpendicular to each other?

   The equipotential lines represent lines that are at the same voltage, or potential energy. The field lines represent the direction of greatest change. The direction of greatest change and direction of no change must be as wide an angle apart as possible, which is perpendicular.

6. Compare a single point charge to a gravitational analog draw or describe a representation. What path must the ball take to stay at the same potential energy? How does this compare to the equipotential lines?

   The ball must travel around the hill, keeping at the same height to stay at the same potential energy level. This compares very similarly to the equipotential field lines of a single point charge.

References

Harris, Norman C. Physics: Principles & Applications; Gregg Division, McGraw-Hill; New York, 1990; 5th ed.