Magnetic Forces and Materials Questions and Answers

Answer: A

Correct answer: the applied field has been reduced to zero

Remanence is the flux density left in a material after it has been saturated and the applied field taken back to zero - the intercept of the hysteresis loop on the flux axis. It is what makes a permanent magnet permanent. Coercivity is the separate quantity: the reverse field needed to bring that remaining flux density to zero.

Answer: B

It is the intercept of the loop on the field axis, and it measures how firmly the material holds its magnetisation. A permanent magnet needs a coercivity of hundreds of kiloamperes per metre; a transformer core needs it as small as possible.

Answer: C

Narrowness means little energy is dissipated per cycle, which is what a core taken repeatedly round the loop requires. Silicon steel and the nickel iron alloys are the standard soft materials, and permanent magnet alloys are their opposite in every respect.

Answer: D

Each traverse of the loop dissipates that energy as heat in the material, so the loss rises in direct proportion to the frequency. Eddy current loss is a separate mechanism and rises as the square of the frequency instead.

Answer: A

The induced voltage driving the eddy currents rises with frequency and so does the resulting current, so the loss goes as the square. Separating the two by measuring total loss at two frequencies is a standard core test.

Answer: B

Thin laminations restrict the area of each eddy current loop and so the voltage driving it, and the loss falls as the square of the lamination thickness. A material of higher resistivity, such as silicon steel or a ferrite, helps for the same reason.

Answer: C

A few per cent of silicon raises the resistivity several fold and also reduces the hysteresis loss, at the cost of making the material brittle and lowering the saturation flux density slightly. The trade has been settled at about three or four per cent for a century.

Answer: D

Cold rolling and annealing align the crystal axes so that the easy direction of magnetisation lies along the strip. A transformer core can be built so the flux follows that direction everywhere, which a rotating machine cannot, and that is why the material suits one and not the other.

Answer: A

Correct answer: the normal component of \( \mathbf{B} \)

This follows directly from \( \nabla\cdot\mathbf{B}=0 \), which admits no magnetic sources anywhere, so no flux can accumulate at a surface and the normal component must pass through unchanged. The normal component of \( \mathbf{H} \) is *not* continuous, since \( B_n = \mu H_n \) and the permeabilities differ - which is what causes flux lines to bend at the interface.

Answer: B

Correct answer: no surface current flows on the interface

From Ampere’s law the tangential components of \( \mathbf{H} \) on either side differ by any surface current density present, so with none flowing the component is continuous. The condition matters in practice: at the surface of a perfect conductor, where surface currents do flow, tangential \( \mathbf{H} \) jumps by exactly that current per unit width.