Frequency Dependence of Maximum Magnetic Field Generated by SpinField Magnetic Field Platform

In any scientific experiment,  it is important to document the physical limits of the apparatus used.  It would be counterproductive to attempt data  collection in a regime where the equipment cannot function properly or at  all.

In our laboratory, constant use of  magnetic fields produced by alternating currents running through magnetic coils  is needed, and it is very valuable to know the extent to which these coils can  produce various field strengths.  We wish  to find the maximum magnetic field strength a given set of coils can produce at  a range of different frequencies.

The circuit used is  essentially a RL circuit consisting of a resistor and an inductor in  series.  The AC source can be assumed to  be a purely sinusoidally oscillating potential difference.

In a series circuit  consisting of a resistor and an inductor, the potential difference across the  entire circuit can be defined purely in terms of the resistance R, the  inductance L, and the alternating current.

After assuming  the current flowing through the circuit is a superposition of sine and cosine  functions, the differential equation can be solved, yielding an expression for  the current in the circuit, as well as its maximum.

Since the current flowing  through the inductor is directly proportional to the magnetic field produced by  it, the maximum field is related to the maximum current by a constant factor.

Afunction generator was set  to output a sine wave with a peak-to-peak voltage of 1.000 V and an offset of 0.000  V.  A resistor of known resistance was  placed in series with the magnetic coils, and a voltmeter was placed in  parallel to the resistor to measure the potential difference across the  resistor (Figure 1).

Potential differences were  measured across the resistor for a time equivalent to 10 periods of AC current  at a given frequency.  A range of  frequencies from .0010 Hz to 200.0 Hz was tested.  Using previous calibration, the calculated  current flowing through the coils was converted to magnetic field strength.  All parameters were controlled and set up  with National Instruments’ LabVIEW software.

Themaximum magnetic field as a function  of AC frequency is shown in Figure 2.  As  can be seen, the highest maximum fields are seen with the lowest frequencies,  decreasing rapidly until an inflection point. After this point, the maximum  field approaches zero slowly as the frequency increases.After fitting the predicted maximum  field/frequency relationship to the data, it is apparent that the theory  matches the experimental results quite well. The data shown in figure 2 differs  from the value of the maximum magnetic field by just a constant.  A simple calibration routine relating current  flow in the circuit to the produced magnetic field would yield the correct  values.

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