THE EXPERIMENT

Purpose

To measure the strength of a magnetic field by two methods based on different physical principles: Faraday's Law and forces on a current element.

Equipment

Permanent magnet assemblies;
lab stand with main unit;
current hairpins of various lengths;
resistor box;
capacitor board;
flip coil on wand;
oscilloscope;
electronic balances (.01 gm and .1 gm resolutions);
small power supply with separate 0-5 amp meter for use with the current hairpin;
centimeter ruler.

A. The force measurement

Measure the magnetic field of a permanent magnet assembly be measuring the force on the magnet as a function of the current in the hairpin between the pole faces. Do this for several hairpins ("L's"). Make a plot showing F vs. I*L, and from a least-squares fit, determine a value of the magnetic field B (with uncertainty).

Hints:

In this method you will place the long, fixed poleface, magnet (partly painted red) on the balance and weigh it. The balance then allows you to push the "tare" button so as to measure only changes from this starting weight.
After connecting the power as diagrammed, make a rough check with moderate current to see that the direction of the current is producing positive weight measured at the scale. If not, reverse the leads at the main unit.

B. The flip coil method

Measure the magnetic field of a permanent magnet using the flip coil technique and compare it to that measured by the force method.

Since the flip coil is too large to fit within the fixed pole face magnets, the magnets with adjustable pole faces are used in this section.

Construct an integrator circuit (Fig. 5) for use with the flip coil. Note that according to Eqn (15) the output voltage is proportional to 1/RC, so a small value of RC is preferred. However, from the discussion leading up to Eqn (14), the flip time must be kept small compared to R₂C. Since R₂C<RC, this latter condition may be quite difficult to obtain if the value of RC is chosen too small.

The pole faces of the permanent magnets are smaller than the diameter of the flip coil so that the magnetic field will not be uniform across the coil. However, the method measures the total flux change in the coil (Eq. 10). If we assume that the field is approximately uniform over the area of the pole faces and zero elsewhere, then equation 11, , (written correctly so as to show both limits of integration) still applies but A must now be the area of the pole faces rather than that of the coils.

Take a series of "flips" and use the resulting values of V₀ to determine a value (with error) for the magnetic field strength.

Hints:

The flip coil axis must be aligned with the magnetic field to avoid introducing a cos factor (where is the misalignment angle) into Eqn (15). To insure accurate coil alignment simply rest the coil against one of the pole faces while "flipping" it.
If the scope trigger is set on "auto" the spot will be sweeping across the screen continuously. If the sweep is slow enough it should be possible to time the "flip" so that it occurs near the center of the display, where it can be easily measured.

Now using the same magnet (with adjustable separation fixed as above) measure the magnetic field strength using the force measurement technique (as in part A). In this case, the adjustable magnet is to heavy for the 0.01 gram balance, and it is necessary to use the 0.1 gram balance and sacrifice some precision in the measurement. Measure the force on the magnet as a function of the current in the hairpin (use the smallest L). Make a plot of F vs I, and from a least-squares fit, determine a value for the magnetic field B (with uncertainty). Compare this value of B with the value obtained using the flip coil technique. Discuss any differences and comment on the accuracy and precision of each method.

Hints:

Unless the loop is much shorter than the diameter of the pole faces, it will not be in a uniform field either. If you have time, you should be able to measure and account for this "edge effect" by measuring the force per unit (horizontal) length of current carrying wire as a function of total horizontal length. In any case, you will need to consider the edge effect when deciding whether the two measurements of the field agree.