Lab-7, Measuring a Magnetic Field
Physics U371/372, Electronics for Scientists, Fall 2007
Don Heiman, Northeastern University (10/26/07)

The magnitude and direction of a magnetic field are important parameters in many laboratory experiments.  The most useful method for measuring a magnetic field relies on the Hall effect, and consequently most "gaussmeters" measure a Hall voltage.  One of the most precise methods monitors the precession of the nuclear spin (nuclear magnetic resonance, NMR).

A simple and straightforward method of measuring a magnetic field (albeit not the most precise) is to measure the voltage induced in a coil of wire (pickup coil), resulting from a change in magnetic flux.  In practice, the flux through the coil is changed by either moving the pick-up coil into the magnetic field, or moving the magnet into the pickup coil.  The magnetic field entering the pickup coil is proportional to the total change in magnetic flux, from an initial flux of zero when the coil is far from the magnet to maximum flux when the coil is fully inserted in the magnet.  Since the flux is related to only these two values and not the details of motion, the magnitude of the field is obtained from the voltage integrated over the motion.

Items needed:

· oscilloscope

· ±15V power supply

· 741 op-amp

· resistors (1 to10 kΩ), capacitors

· insulated copper “magnet” wire

· small "refrigerator magnet," high-field permanent magnet

I. Experiment Design – Before constructing the pickup coil and an integrating op-amp circuit, some tests and "back of the envelope" calculations should be made to determine the design parameters.

First, the magnetic-field-induced voltage from the pickup coil must be larger than the drift of the integrating circuit.  Choose values for N (number of turns), and A (area of constant flux within the pickup coil).  Compute the voltage (V_in) you would expect for a field of B=1/10 tesla.  Is V_in significantly larger (10X) than the input bias voltage for the 741?  If not, increase NA.

Second, make sure the computed op-amp voltage output is larger than the typical noise level, V_o > 20 mV, by the choice of C and R=1 to10 kΩ.
        Construct an integrating circuit (make sure you have the two wires for discharging C).
        Measure the output voltage drift (dV_o/dt) of your circuit and discuss.
        Discuss why you choose N, A, and C.

II. Measurements – Test the integrating circuit by moving the "refrigerator magnet" near the pickup coil.  You should see the voltage change on the scope when the magnet is brought close to the pickup coil.

Quickly insert then remove the pickup coil between the pole pieces of the large magnet and remove several times.  Record the voltage changes in V_o on the scope and make a copy.
        Compute B for the large magnet from V_o, N, A, and the measured values for R and C.
        Compute B for the "refrigerator magnet."
        Q: How well does your device work?  How could you improve the device?

Construct a differentiating circuit.
        Q: What happens when the "refrigerator magnet" is quickly brought near the pickup coil?
        Q: How could this be used on a bicycle wheel to measure the speed of the bicycle?