Day 6: Map Field of Current
Lesson Plan

Goal of Lesson:
Establish that moving charges create a magnetic field. Establish that the speed and direction of motion, the amount of charge, and the deflection angle observed are closely linked.

Basic Procedure Part 1:

• Blow up a balloon.
• Rub against hair or otherwise place static charge on balloon.
• Move balloon while it is near magnetometer.
• Show deflection is induced but it is perpendicular to plane of motion.

Basic Procedure Part 2:

• Connect a simple DC circuit. Use V=IR to establish current for a given potential. Either use a variable voltage source and constant resistance or a constant voltage source and a variable resistor.
• Show a current causes a deflection perpendicular to plane of current and show the direction can be predicted if sense of potential difference is known.
• Show that the amount of deflection is reduced when the distance between the magnetometer and line current is increased while the current is held constant.

Basic Procedure Part 3:

• Connect a loop of wire to a reasonably sensitive voltmeter.
• Show a moving magnet produces a potential difference in a wire.

Learning Goals

• The students will investigate through short hands-on activities how a magnetic field is produced.
• Students will use the magnetometer built on Day 2 and several familiar phenomena.

Assumed background:
It is assumed the students have experience with simple circuits and Ohm's Law. If not, I recommend the required circuits are set up in advance and a conversion table relating the input variable (resistance or potential across circuit) to the output variable (current) be supplied.

Part 1

Students know that a balloon can acquire a static charge if it is rubbed against their hair or certain materials. Have the students do this and then hold the balloon near the magnetometer. If they are holding it still they will not see a deflection. The students will then be asked to move the balloon in specified ways. Ask them to find a way to get a deflection from the magnetometer using only the balloon and making no contact with the magnetometer. They should discover that moving the balloon vertically produces a sideways deflection. They should discover that moving the balloon up produces the opposite deflection as down. They should discover little or no deflection if the motion is parallel to the plane of rotation of the magnetometer. If they are careful, they may discover that when the balloon and magnetometer are moving but have no velocity relative to each other, no magnetic field is observed. This is a tricky measurement and the magnetometer was not designed with this in mind.

Encourage the students to try different parts of the balloon (sides, both ends, and so forth). Of course, remember to discharge the balloon between trials. The greater the curvature of the part given electrostatic charge, the more of a deflection a given motion of the balloon will produce.

It is possible to move the balloon so fast that no deflection is seen even though a slower motion produces a strong deflection. This can be explained using inertial considerations.

Other static charge devices could easily be substituted for the balloon. Using the glass rod and silk set-up might make it easier to control, but would make it harder to work out the curvature effect on local potential fields.

Students ought to try diagonal motion relative to the plane of rotation also. The goal is to establish that the vertical component of the charged particle motion relative to the magnet is what produces a horizontal deflection.

Part 2-3

Students will work with a circuit producing a known DC current and measure the magnetic field induced by a long straight wire. The wire will need to be oriented vertically to be most convenient for magnetometer readings. Appeal to symmetry to simplify data taking. (Mapping one hemisphere of the field around a wire ought to be sufficient.)

Work with circles of increasing radius to make the maps for different radial distances. That is, the students will move the magnetometer in the "theta direction" while keeping a constant radial position. This is an opportunity to work with polar coordinates explicitly, if you so choose.

This is an opportunity to measure field strength by using the pendulum with a magnet on it. Students (who have worked with Newton's 2nd Law and free body diagrams) can measure the strength of the magnetic field produced by the current. The magnitude of the magnetic force will be the product of the weight of the pendulum magnet and the tangent of the deflection angle of the pendulum from the vertical. Students can measure the angle with a protractor and measure the mass of the magnet quite easily. A graph of magnetic force as a function of current (keeping the pendulum a constant distance from the current) should show a linear form. Students may need reminding that it is the shortest straight line distance from the position of the pendulum magnet to the current carrying wire that is to be measured and plotted. A graph of magnetic force as a function of the distance of the pendulum magnet from the line current ought to show a (1/r) dependence when the current is held constant.

These two graphs can then be combined to yield the statement that the magnetic field of a long straight current carrying wire is proportional to the ratio of the current and distance from the current carrying wire.

Next, have the students form a vertical loop in the wire and measure the direction of the magnetic field outside the loop.

The goal is to motivate the right hand rule for field direction relative to the current in a wire.

Part 4

The final step is to use a (changing) magnetic field to produce a potential difference. The set-up should be a circuit with voltmeter. A galvanometer would also work well in the place of a voltmeter. If the student moves a reasonably strong magnet near the wire, a potential will be measured as a deflection of the voltmeter. This indicates a current is flowing in the wire. The current will only flow when the magnetic field around the wire is changing (that is, when the source magnet is moving). Students ought to play with this some to discover that the magnetic field strength must change as a function of time to produce a current. This can be achieved by moving a permanent magnet near the wire in such a way as magnetic field lines are "cutting" the wire. The students ought to find that the deflection of the galvanometer is maximized for speed of movement of the magnet and for strength of magnet. A set-up that induces larger deflections is to place a 1-2 inch diameter solenoid in the circuit and to move a bar magnet in and out of the solenoid core region. Another set-up that may provide more control is to have a small Helmholtz coil as the magnet.

We note that this is an explicit application of the re-mapping of magnetic fields done in previous activities.

Part 5

Discussion points to bring out:

• Right hand rule is revealed by the above activities.
• The symmetry of the process:: a current (or flow of charges) induces a magnetic field while a changing magnetic field induces a current.
• The relative conductivity of the material they are working with affects the observation. After all, moving a large magnet near a piece of wood still induces a potential difference. The potential difference does not produce a current as the wood has very low conductivity (essentially no free electrons.)

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Lesson Development/Writing: Ed Eckel
Web Design: Theresa Valentine
Last Updated: 8/25/2000