Day 3: Mapping a Dipole Magnetic Field
Lesson Plan

Students will work cooperatively (groups of 2) using the magnetometer built in the previous class to discover the shape of a magnetic field due to a bar magnet. Such a field is called a "dipole field." Note: At this point the students have not been formally introduced to the term "magnetic field."

Objective:
Students will use the magnetometer to map the field of a bar magnet. The map will indicate direction of field only, and will resemble a 'dipole field' once the magnetic field of the earth is subtracted from the observations.

Student Outcomes:

• Students will collect data using a student made magnetic field detector (magnetometer.)
• Students will work in cooperative groups
• Students will graphically represent the data.
• Students will interpret the graphical representation of the data.
• Students will report and discuss class results.

Materials:

• Bar magnet.
• Three different color markers or pencils.
• 3-4 sheets of poster paper, at least 2 ft on edge, per group.
• Magnetometer as built in Day 2 Lesson.
• Tape.

Opening Probing Question:
Where does a magnetic force begin and end in the space around the magnet?

Suggested Response:
We (the class) do not know yet. Some may know the field representation uses closed loops. Others may argue that the force begins on the magnet and ends on the object experiencing the force. Perhaps challenge the response with a request to apply Newton's Third Law to the explanation and then ask what is meant by the words "begin" and "end". Is there a material object or thing that accepts magnetic force like an electric light bulb accepts current?

Opening Discussion:
Recap the investigation done on Day 1. Recall that we knew a magnet was affecting another object by the motion induced in the object (moved away from or toward magnet) or by the fact that the object did not fall in a gravitational field when placed against the magnet. Both of these are examples of thinking with Newton's Laws, of course.

Remind students of vectors. The nature of motion and force is that each requires two elements for a complete description: direction and quantity. That is, motion and force are both intrinsically VECTOR quantities.

Close discussion by asking students if magnetism demonstrates vector or scalar characteristics.

Hand out materials and student activity pages.

Activity 1

Goal:
Obtain a good quality representation of the total magnetic field around a bar or dipole magnet.

Data Collection Procedure:

• Along all edges of the paper, mark points separated by 10cm and draw a grid on the paper.
• Place the paper on a lab desk. Use tape to mark the edges of the 4 corners so that you could place another paper in exactly the same position.
• Place bar magnet horizontally in center of paper. Tape magnet to paper. Outline and mark where the bar magnet is relative to the grid on the paper.
• Use the magnetometer to determine the direction of the magnetic field at each grid point.
• Record the direction of alignment by drawing a short directed line segment that accurately shows the direction the detector magnet is pointing at that location. The line segment should be centered on the point directly below the center of the magnetometer and should be about an inch long.
• Repeat at each grid intersection.
• Put a legend on the completed map which includes information about the orientation of the map relative to some fixed reference point in the room (a wall clock or a door for instance).
• Put a title on the map as follows: Bar Magnet Map, date, and your group identification

Data Analysis Questions to be Done by Small Group

• Are all the arrows pointing in the same direction? Explain why you think your data is correct or incorrect.
• If I bring one magnet near the magnetometer, the magnetometer deflects. If I bring two magnets near the magnetometer but at different locations, will I measure the combination of the effect of the two magnets or just the effect of one of them? Write a convincing argument!
• While gathering data, did you record the effect of just the bar magnet or the bar magnet and some other things? Name the sources of all effects. Look closely at the lab table for possible answers. Consider the materials you worked with the first day of the magnets unit for hints.
• Can you subtract or otherwise remove the unwanted effects to get the effect of just the bar magnet? Explain your answer.

Class Discussion
The goal of this discussion is to arrive at the following understanding. Recap the questions given in the activity to achieve this.

The students have mapped the magnetic field of a bar magnet. They have found some anomalous observations as well as some fairly consistent patterns. The consistent pattern is called a dipole field map. By comparing maps between groups, the differences in recorded observations ought to inspire some examination of the data collection procedure. Differences may be due to current carrying wires, to chunks of metal, and to other magnets in the vicinity of the mapping location. Further, all observations have picked up a small contribution from the earth's magnetic field. The variations should be different at different locations in the room due to the strength of the bar magnet used, the orientation of the grid system relative to magnetic north, and limits to the precision with which observed deflection is represented on the grid. The contribution of the earth is approximately the same at every point in the room. One of the difficulties with the earth contribution is that it is weak. Therefore, it has an increasingly important effect as you move farther from the bar magnet in the center of the map.

Generate the following consensus: To get the actual map of the field of a bar magnet, we must know what the 'ambient' local field looks like in the absence of the bar magnet. We can then compare the total field to the ambient field (from Activity 2) to determine the actual bar magnet field.

Suggested Questions for Discussion
Does your bar magnet map reveal just the effect of the bar magnet or is the map revealing a complex combination of different effects.

The first map, done as directed, reveals the superposition of the field of the earth and the bar magnet. If different groups had their bar magnet at different orientations relative to some fixed object in the room, different groups may have maps with different appearances.

Chemists describe the extent of an electron cloud in terms of the point where 90% of the electron density is within some radius. Can you find a similar position on your grid, where 90% or more of the observation is due to just the bar magnet? How are you assigning magnitudes to the observed direction measurements? The analogy is possible but this is a deep question some students may not be prepared for. The purpose of the question is to help instill a sense of familiarity with the idea of combinations.

Activity 2

Purpose:
Obtain representation of ambient magnetic field at location of Activity 1.

Data Collection Procedure:

• Place a clean sheet of paper in exactly the same location as in Activity 1.
• Draw a 10cm grid on it.
• Without any other magnets near by, place the magnetometer at each grid intersection and record the direction of its alignment with a 2nd color marker.
• Put a legend on the completed map which includes information about the orientation of the map relative to some fixed reference point in the room (a wall clock or a door for instance).
• Put this title on the map: Earth Magnet Map, date, and your group identification

Data Analysis Questions for Small Group

• Are all the arrows on the Earth Magnet Map pointing in the same direction? Explain why you think your data is correct or incorrect.
• Are any adjacent arrows pointing in approximately the opposite direction? Propose a test on for such variations.
• Under what conditions can the effect of a magnetic change?

Class Discussion:
Goal: While recapping the questions for Activity 2, achieve the following motivation for the next Lesson Plan (Day 4).

We need to remove the effect of the earth's field from the observations to get a true representation of the field of a bar or dipole magnet. We can do this one of 2 ways. One is to visually subtract by comparing the direction of the arrow in Activity 1 to the direction of the arrow in Activity 2 at the same grid position. Another is to rotate the bar magnet 90o, record a map of the new field shape, and compare the result with Activity 1. We will do both of these during the next class.

Suggested Discussion Questions:

• Does the Earth Map influence how you interpret the Bar Magnet Map? How far from the bar magnet does the effect of the bar magnet disappear? This is a convenient predict and check question that reveals a common problem that arises in science. We are measuring the bar magnet field while immersed in the earth's magnetic field. Thus, one must work to remove the extra field (the earth in this case) in order to reveal the true field of the bar magnet. As one gets farther from the source, the magnetic field of the earth begins to dominate and produce a nearly uniform magnetic field. The key is to determine the field of the earth, and to subtract it from the measured field to reveal the field of the bar magnet. Fortunately, the field of the earth is very weak (10-5 gauss) while the field of the bar magnet is relatively strong (10-100 gauss) and thus the earth's field does not need to be removed until you get out to several lengths of the bar magnet. This question gets back to a fundamental part of magnetism: a dipole field depletes as the inverse cube of the distance between the dipole and the measurement location. Magnetic fields are not infinite in extent, like gravitational and electrostatic fields.
• Can the observation be made in such a way that the effect of the earth's field on the observed bar magnet field is eliminated? Consider aligning the bar magnet along magnetic north, making a map, re-aligning with bar magnet aligned opposite earth's magnetic field, observe and record that field, and take the "average of the two" to remove the superposition of the earth's magnetic field on the observed field. Alternatively, compare 2 maps made with the bar magnet at 90o relative orientations (N-S versus E-W.)
• If we are always immersed in the earth's magnetic field, how can we be sure we are detecting just the magnetic field of the object or magnetic phenomenon we are studying? This is one of the above questions rewritten. Simply, we expect to see a certain phenomenon and see something different when a particular new element is added to the system. The change is correlated to the added element. We modify the element (say, by halving and by doubling it) and observe changes in the effect produced.

Homework Suggestion:
Read about the interaction between the solar wind and the earth's magnetic field.

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Lesson Development/Writing: Ed Eckel
Web Design: Theresa Valentine
Last Updated: 8/11/2000