Magnetic Circuits Questions and Answers

Answer: C

The unit of mmf is the ampere turn.

Magnetomotive force is the driving force that sets up flux in a magnetic circuit, and it equals the current multiplied by the number of turns it flows through: mmf = NI. Its unit is therefore the ampere turn (AT), often written simply as ampere in SI.

The weber is the unit of flux, the weber per square metre (tesla) is the unit of flux density, and the ampere turn per metre is the unit of magnetising force H, which is mmf per unit length.

Answer: B

The self-inductance is 4 H.

Self-inductance is the flux linkage per ampere: \(L = N\Phi / I\).

\[ \begin{aligned} L &= \frac{2000 \times 4 \times 10^{-3}}{2} \\ &= \frac{8}{2} = 4\ \text{H} \end{aligned} \]

Forgetting to divide by the current gives 8 H, which is not offered; 2 H and 1 H come from dividing by the wrong quantity.

Answer: B

No emf is produced when the magnetic field is in the same plane as the coil, whether or not it varies.

An emf is induced only if the magnetic flux through the coil changes. Flux is the field component perpendicular to the coil's plane multiplied by the area. If the field lies entirely in the plane of the coil, no field lines pass through it, so the flux stays zero however much the coil expands or the field changes.

A constant field with a perpendicular component, as in options A and D, would give an increasing flux as the area grows, and so an emf. A perpendicular component that is increasing would add to the change in flux rather than cancel it.

Answer: A

A high permeability material helps to confine the flux within the magnetic circuit.

Permeability measures how easily a material carries magnetic flux. A core of high permeability has a low reluctance, so almost all the flux set up by the winding follows the core instead of leaking through the surrounding air. That is why transformer and machine cores are made of high-permeability steel.

It reduces leakage rather than allowing it, and it does not itself produce current or voltage; it only lets a given mmf produce more flux.

Answer: A

Once the flux is set up, no further energy is required to maintain it.

Energy is needed only while the flux is being built up; it is stored in the magnetic field. After that, a steady flux requires no further energy input, just as a steady current in an ideal inductor needs no voltage. In a real coil the only continuing loss is the I²R heat in the winding's resistance, which belongs to the electric circuit, not the magnetic one.

This differs from the electric circuit, where current flowing through resistance consumes energy continuously. A steady magnetic flux does not release energy as heat or light.

Answer: C

The mutual inductance is 0.25 H.

Two coils in series have a total inductance \(L_{1} + L_{2} \pm 2M\), the sign depending on whether their fluxes aid or oppose. So the two given values are:

\[ \begin{aligned} L_{1} + L_{2} + 2M &= 1.2 \\ L_{1} + L_{2} - 2M &= 0.2 \\ 4M &= 1.0,\quad M = 0.25\ \text{H} \end{aligned} \]

The 0.4 H of one coil is not needed for M; it only gives the other coil as 0.3 H. 1.0 H is 4M, not M, and 1.4 H is the sum of the two series values.

Answer: C

The highest permeability belongs to ferromagnetic material.

Ferromagnetic materials such as iron, nickel and cobalt have relative permeabilities from hundreds to many thousands, because their magnetic domains line up strongly with an applied field.

Vacuum has a relative permeability of exactly 1 by definition. Paramagnetic materials are only slightly above 1 and diamagnetic materials slightly below 1, so none of them comes close.

Answer: A

The correct matching is (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i).

• Bismuth is the classic diamagnetic material, with a relative permeability slightly below 1: (a)-(iv).
• Aluminium is paramagnetic, slightly above 1: (b)-(iii).
• Iron is ferromagnetic: (c)-(ii).
• That leaves neodymium, whose neodymium-iron-boron alloys make the strongest permanent magnets, for the paper's 'supermagnetic': (d)-(i).

The first three pairs are standard, and only one option has all three. The other options put aluminium with diamagnetism or neodymium with ferromagnetism in place of iron.

Answer: A

Such a material is called a diamagnetic material.

In a diamagnetic material the induced magnetisation opposes the applied field, so the magnetic susceptibility is small and negative and the relative permeability is slightly less than 1. Bismuth, copper, silver and water are examples.

Paramagnetic materials have a relative permeability slightly greater than 1, and ferromagnetic and ferrimagnetic materials have relative permeabilities far greater than 1, so none of them fits.

Answer: C

The magnetic analogue of conductance is permeance.

A magnetic circuit is treated like an electric one: mmf corresponds to emf, flux to current, and reluctance to resistance, giving flux = mmf / reluctance. Conductance is the reciprocal of resistance, so its counterpart is the reciprocal of reluctance, which is permeance.

Reluctance is the analogue of resistance, not conductance. Flux is the analogue of current, and permeability is the material property that corresponds to conductivity, not to the conductance of a whole circuit.