AAPT Apparatus Competition, Entry Description

Introductory Laboratory Category

Apparatus Title: Connecting Electricity and Magnetism in One Apparatus.

Introduction:

An important feature of the second semester of many introductory physics courses is the interplay between electricity and magnetism. In the laboratory, the study of the creation of magnetic fields by electric currents and the creation of electric currents by magnetic fields are well suited to introductory students. These effects are large enough to measure directly with simple modern equipment such as a hall probe and analog to digital converters directly monitored by a computer. The pedagogical challenge is to convince students that they are dealing with a single theory, not a collection of disconnected formulas. Because novices typically focus on the surface features of any situation, as opposed to the underlying principles, this tendency is reinforced if the student laboratory experience is based on using different apparatus to explore each electromagnetic effect. The underlying aim of this apparatus is to place the student in a laboratory environment that emphasizes the unity of the underlying principles by presenting them in an identical physical context. Using essentially the same apparatus to study many different effects, Table 1, has the additional advantage of minimizing the time students need to take to become familiar with any equipment. It also minimizes the cost of the laboratory equipment. The basic component of this apparatus consists of two identical parallel circular coils of wire, whose planes are separated by a distance equal to their radius. This Helmholtz coil configuration was chosen to give a region of uniform magnetic field so that magnetic effects on charges or currents can be straightforwardly calculated by students. We wish to emphasize that the components of this apparatus and the physics principles illustrated are very traditional in introductory physic instruction. The parts are common and the assembly is straightforward. The strength of this apparatus is its versatility, simple operation, and ruggedness. These virtues make it ideal to include in any physics laboratory that emphasizes the unity of physics.

Description:

Based on these considerations, we have developed a simple, sturdy, and relatively inexpensive apparatus, parts and costs are given in Table 2, that can be used to explore a wide variety of the physical principles that comprise about half of the second semester of our introductory physics course. In our pedagogy these applications are posed as problems, but the usefulness of the apparatus is independent of the exact nature of the pedagogy employed. The apparatus, shown in Figures 1 - 4, consists of a 27 cm X 34 cm X 17 cm Lucite box inside of which are mounted two coils each with a radius of 12.5 cm separated by 12.5 cm. 6.5 cm diameter holes in the box and its two open sides allow easy access to the components for measuring the magnetic field, connecting the coils in different electrical configurations, and inserting a pick-up coil or an electron gun (CRT). Note that this device is not significantly different than other such devices such as from PASCO (EM-6715 with EM-6711) except: (1) our configuration is significantly more rugged and easier for novice students to use, (2) our rotating coil has mercury bearings to give a smooth electrical response without the noise generated by contact connections. Although our current version of this apparatus does not allow for changing the distance between coils, it could be easily modified to do so.

Table 1: The physics that the students explore with this apparatus.

Lorentz Force: (Helmholtz coils with CRT and Hall Probe)

Torque on a current loop: (Helmholtz coils with hall probe, ammeter, and pick-up coil)

Biot-Savart Law: (One coil, two coils with hall probe, ammeter)

Ampere’s Law: (One coil with hall probe, ammeter)

Faraday’s Law: (Helmholtz coils, hall probe, voltmeter, rotating pick-up coil or stationary pick-up coil with oscillating Helmholtz coil current)

Flux: (Helmholtz coils, hall probe, voltmeter, stationary pick-up coil and oscillating Helmholtz coil current)

Table 2: Parts and Costs of Constructed Apparatus:

1 sq. meter of ½” thick Lucite $ 65

1 12 volt dc 0-3000 rpm motor $ 12

37 gauge insulated copper wire for 3000 turn pick up coil $ 15

18 gauge insulated copper wire for 150 turn Helmholtz coils $ 27

bolts, screws and banana jack inserts $ 10

motor mount parts (aluminum for bearings, base plate, epoxy, Lucite, drive belt) $ 45

2 mercotac bearings (model 110T) $114

The Cathod Ray Tube, Hall Probe, Dual Channel Amplifier, Digital Voltmeter, Computer Interface, Computer, Power supplies, and connecting wires are purchased separately and are available from laboratory supply companies.

Figure 1 – Magnetic Fields Caused by Electric Current.

Figure 1-a: Apparatus configured to measure the magnetic field caused by a constant current either through one or two coils of wire.

Figure 1-b: Measurement of the magnetic field along the axis of the coils, when the current is 3 amps. The points with error bars are the measurement and the curve is the calculation using the Biot-Savart Law. The agreement is excellent with small deviations due to the coil spacing not being exactly in the Helmholtz configuration. The magnetic field between the coils is independent of position to a very good approximation.

Figure 2 – Deflection of Electrons in a Magnetic Field

Figure 2-a: Apparatus configured to measure the deflection of electrons caused by a constant magnetic field.

Figure 2-b: Measurement of the deflection of an electron beam as a function of the magnetic field from two coils in a Helmholtz configuration. The points with error bars are the measurements of the deflection with a ruler and the magnetic field with a Hall Probe. The straight line is the prediction using the Lorentz Force Law.

Figure 3 – EMF produced by changing magnetic flux.

Figure 3-a: Apparatus configured to measure the current in a pick up coil caused by a time varying magnetic flux. Either the pick up coil is stationary and the current in the Helmholtz coils oscillates or the pick up coil is rotated by the electric motor and the Helmholtz coil current is constant.

Figure 3-b: Measurement of the voltage difference across the pick up coil as a function its rotational frequency in a magnetic field generated by the Helmholtz coil configuration. The points with error bars are the measurements and the straight line is the prediction from Faraday’s Law.

Figure 4 – Apparatus Set-up on a Laboratory Table.

Constructing a Lucite Helmholtz Coil:

The apparatus consists of two separate parts. The Helmholtz coil and the induction motor.

Assembling the Helmholtz coil:

Machine bottom, sides, top and center cross plate to specs on pages 1-4 of the engineering schematics. Assembly of box is done using epoxy.

Coils for the box are spooled on a lathe with the jig set to a radius of 12.25 cm. The 150 coils of 18-gauge wire bring the average radius of the complete coil to 12.5cm. They are held together with zip ties. The coils are secured inside of the box using 3.5cm X 7.5cm flaps of clear plastic secured with 6-32 screws.

Assembling the “motor”

All parts are machined to the specifications on pages 6-13 of the engineering schematics and assembled as shown on page 5.

The generator coil is spooled on a lathe using the jig shown on page 13 of the schematics. With the 3000 coils of 37-gauge wire spooled on the jig, the coil is tied off using thread and placed inside of the channel of the coil plate shown on page 6 of the schematics. The ends of the coil are soldered to the collars shown on pages 7 and 8 of the schematics. The coils are secured by filling the entire channel with epoxy after all connections are made.