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Lab V, Problem 5 Determining Magnetic Field of a Coil

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Abstract:

The object of this lab was to determine the relationship between the strength of a the magnetic field of a Helmholtz coil and the distance from the coil, along its central axis. Calculations for this relationship are in the predictions section below. The field was measured at eleven different points (5 on each side and one in the center) and recorded using a Hall Probe.

Introduction:

The example given in the Lab Manual1 was for studying bacteria. Helmholz coil was to be used as a model to be used to mimic and quantify the behavior of magnetotactic bacteria in an environment in a magnetic field. A Helmholz coil will stand in place, to create the magnetic field lines and a Hall Probe and Magnet Lab software will be used to measure the strength of the field at varying distances.

Prediction:

Using the Biot-Savarte Law for a B-field of a current:

[pic]
Where μo is the permeability of free space.

And the formula for magnetic flux through a surface:

[pic]

A formula to relate the strength of a magnetic field (B) in relation to the distance away from it (x)

[pic] [pic] sin θ goes to 1

[pic]

With the following substitutions:
[pic] and [pic]
(see Fig 1 below)
We can then derive our final equation:

[pic]
N being the number of coils in the Helmholtz

Fig 1: Geometrical proof of the substitutions used in the above formulas where dL is tangent to the circle.

Fig 2: Front view (a) and side view (b) of experimental set-up. A Helmholtz coil was set up on a table top and connected to a power source. The Hall Probe was calibrated according to the Lab Manual1 and held atop a wooden block at varying distances (x) from the center of the coil. Eleven measurements were taken: 5 from the "positive" side, one in the center, and 5 from the "negative" side of the coil.

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