Magnetic Circuit Design:

demagnetizing field.

by Dr. Peter Campbell

In the previous Section we introduced the concept of recoil operation and showed how temperature changes could induce a magnet to operate on a recoil line, which is part of a minor magnetization curve. Now we are going to see that irreversible loss causing the same effect can result if an unfavorable demagnetizing field is applied to a magnet.

For the same simple magnetic circuit we used in Section 4A, we have added a coil (shown above) with N turns carrying current i, whose direction here is chosen such as to hinder the magnet (area A_m , length l_m) from delivering flux into the air gap (area A_g , length l_g). As before, we choose to integrate the magnetizing force H around the closed loop shown in red, only now this loop links N times with the current i. Ampère's Law, and the derived magnetic circuit equations shown here must include this source term.

Using the original flux conservation equation, the load line expression now contains an additional term representing the demagnetizing field of the coil. The slope B_m/H_m of the load line is unchanged, but its position is determined by the coil excitation Ni/l_m as shown in the diagram below.

If the coil's demagnetizing field increases incrementally and then decreases again to its original value, even cycling through these values, the magnet's operating point will run down and up the demagnetization curve in the manner shown in the B vs. H diagram below. But this is at room temperature, where this material suffers no apparent irreversible loss of its magnetization.

Now consider that a changing coil excitation cycles the load line through the same range, but with the magnet now operating at +60^oC rather than +20^oC. The diagram below shows that, at the greater demagnetizing fields, the operating point passes the "knee" and the magnet does suffer an irreversible loss of its magnetization. The operating point cannot return up the major demagnetization curve, but will follow a path within this characteristic. Since an irreversible loss has occurred, the magnet can only be returned to its original condition if it is fully remagnetized.

Notice that while the excursion of the load line is proportional to the coil's excitation Ni, it is also inversely proportional to the magnet's length l_m. Additional magnet length can apparently be used to stabilize a magnet against irreversible loss in two ways:

it raises the slope of the load line, so the magnet's operating point at any temperature is further away from the "knee";
for a given coil excitation, it reduces the rate at which the load line approaches the "knee" (with its associated loss of magnetization).

The price of such temperature stability is, of course, the use of additional magnet material.