Rotational Behavior of a Magnetic Torsion Pendulum in a Helmholtz Coil

Cody Goolsby∗

Department of Physics, University of Southern Maine96 Falmouth Street, Portland, ME 04104-9300

(Dated: November 16, 2011)

A Helmholtz coil is traditionally used if one wants to produce a uniform magnetic field over a given volume of space.As shown in Fig. 1, a Helmholtz coil consists of loops of wire seperated by the radius of the loops.

FIG. 1: A Helmholtz coil. FIG. 2: Compass aligning itself with the Earth’s magnetic field.

When a current is supplied through the wires a relatively uniform magnetic field is produced in the center of coils.Such a Helmholtz coil was used in an intermediate physics lab to determine the torisonal constant, moment of inertia,and other variables for a magnetic torsion pendulum (MTP). During the lab session, we noticed obstensibly abberantrotational behavior of the MTP which devianted from how we expected the MTP to behavior. Our MTP nominallyacts just like a compass in the Earth’s magnetic field as shown in Fig.2. The Earth’s field can be parsed out into itshorizontal and vertical components (Fig. 3).

FIG. 3: Vector rendering of the Earth’s horizontal and vertical magnetic field.

For the pendulum we were working with, it would initially align itself with the horizontal component of the Earth’sfield when there was no current in the Helmholtz coils (Fig.4 and Fig.5).

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FIG. 4: Pendulum in the Earth’s field. FIG. 5: Alignment of pendulum in the Earth’s field.

We then thought as we increased the current in the Helmholtz coil the Earth’s magnetic field would be cancelledout by the coil’s field, thus causing the pendulum to flip (Fig.6 and Fig.7).

FIG. 6: Pendulum aligning with the coils field after nulling outthe Earth’s field.

FIG. 7: Pendulum ligned with the net magnetic field from thecoils and the Earth’s magnetic field.

We expected as the current was increased in the Helmholtz coil that the pendulum would flip around instantly assoon as the coil’s field overpowered the Earth’s field. Instead we observed the pendulum slowly rotating and not as wepredicted an instanteous alignment with the persumed nulled out Earth’s field. In order to investigate this seeminglyabnormal behavior we needed to have a complete picture of the interplay between the Earth’s and Helmholtz coil’smagnetic fields between the coils.

∗ Electronic address: cody.goolsby@maine.edu