Thirty multiple choice questions on dipoles, the Earth’s field and magnetic materials. No question from this chapter appeared in the papers I could extract, so every question here is built to the AAI pattern and to the difficulty the domain section has shown elsewhere.
30questions
35 minsuggested time
0verified PYQs
MCQformat throughout
Score0 correct · 0 of 30 attempted
Before you begin
Formulas you will need
Key formulas
Magnetic moment of a current loop: m = NIA · Torque: τ = mB sinθ · Potential energy: U = −mB cosθ
Axial field of a dipole: μ02m ∕ 4πr³ · Equatorial field: μ0m ∕ 4πr³
Earth's field: BH = B cosδ · BV = B sinδ · tanδ = BV ∕ BH
B = μ0(H + M) · χ = M ∕ H · μr = 1 + χ · Curie law: χ ∝ 1 ∕ T
How to use this worksheet. Torque uses sine of the angle and potential energy uses cosine — mixing those two accounts for most lost marks in this chapter. For the Earth’s field, remember that dip is measured from the horizontal, so BH = B cosδ.
Section A · Level 1
Dipoles, Earth's field and classification
Ten questions. None should take more than twenty seconds.
Q1
The magnetic moment of a current loop of N turns, area A, carrying current I is:
Magnetic moment is m = NIA, directed along the normal to the loop as given by the right hand rule.
Q2
The net magnetic flux through any closed surface is always:
Gauss's law for magnetism states that the net flux is zero, because magnetic field lines always form closed loops. This is the formal statement that isolated magnetic poles do not exist.
Q3
An isolated magnetic monopole:
Cutting a magnet in half simply produces two smaller dipoles. No isolated north or south pole has ever been found.
Q4
The angle between the geographic and magnetic meridians at a place is called the:
Declination is the horizontal angle between true north and magnetic north. Dip, also called inclination, is a vertical angle instead.
Q5
The angle of dip at the magnetic equator is:
At the magnetic equator the Earth's field is horizontal, so the dip needle stays level and the dip is zero. At the magnetic poles the dip is 90°.
Q6
Substances that are weakly repelled by a magnetic field are called:
Diamagnetic materials develop a magnetisation opposing the applied field, so they are weakly repelled. Bismuth and copper are examples.
Q7
The magnetic susceptibility of a diamagnetic material is:
Diamagnetics have a small negative susceptibility, typically of order −10−5, which is why their relative permeability is slightly less than one.
Q8
Which of the following is a ferromagnetic material?
Iron, cobalt and nickel are the common ferromagnets. Copper and bismuth are diamagnetic and aluminium is paramagnetic.
Q9
The relative permeability of a material is related to its susceptibility by:
μr = 1 + χ. For diamagnetics χ is slightly negative so μr is just below one; for ferromagnets χ is huge so μr is very large.
Q10
The SI unit of magnetic moment is:
Since m = NIA, the unit is ampere times square metre.
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Section B · Level 2
Torque, dipole fields and temperature
Ten questions. Watch whether the formula needs a sine or a cosine.
Q11
The torque on a magnetic dipole of moment m placed at an angle θ to a field B is:
τ = mB sinθ, which is maximum when the dipole is perpendicular to the field and zero when it is aligned with it.
Q12
A magnetic dipole of moment 0.5 A m² is placed at 30° to a field of 0.2 T. The torque on it is:
τ = mB sinθ = 0.5 × 0.2 × sin 30° = 0.5 × 0.2 × 0.5 = 0.05 N m. Option 3 uses cos 30° instead of sin.
Q13
The potential energy of a magnetic dipole is minimum when it is:
U = −mB cosθ, which is most negative at θ = 0. An aligned dipole is therefore in stable equilibrium; the anti-parallel position is unstable.
Q14
At the same distance from a short bar magnet, the ratio of the axial field to the equatorial field is:
The axial field is μ02m ∕ 4πr³ and the equatorial field is μ0m ∕ 4πr³, so the axial field is twice as strong.
Q15
The field of a short bar magnet falls off with distance as:
A dipole field falls as the inverse cube of distance, unlike the inverse square of a point charge.
Q16
If the angle of dip at a place is 45°, then the vertical and horizontal components of the Earth's field are:
tanδ = BV ∕ BH, and tan 45° = 1, so the two components are equal.
Q17
At a place the horizontal component of the Earth's field is 0.34 G and the dip is 60°. The total field is:
B = BH ∕ cosδ = 0.34 ∕ cos 60° = 0.34 ∕ 0.5 = 0.68 G.
Q18
When a bar magnet is cut into two equal halves perpendicular to its length, each piece has:
Each half keeps the same pole strength but has half the length, so its magnetic moment is halved. Both halves remain complete dipoles.
Q19
The susceptibility of a paramagnetic material varies with absolute temperature as:
Curie's law states that paramagnetic susceptibility is inversely proportional to absolute temperature, since thermal agitation disrupts the alignment of the dipoles.
Q20
Above its Curie temperature, a ferromagnetic material becomes:
Thermal energy destroys the domain structure at the Curie point, and the material behaves as a paramagnet from then on.
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Section C · Level 3
Magnetic materials and hysteresis
Ten questions. Each needs a material property plus a piece of reasoning.
Q21
The magnetic field inside a perfectly diamagnetic material such as a superconductor is:
A superconductor expels the field entirely, so χ = −1 and μr = 0. This is the Meissner effect.
Q22
The property by which a ferromagnetic material retains some magnetisation after the applied field is removed is called:
Retentivity is the magnetisation remaining at zero applied field. Coercivity is the reverse field needed to remove that remaining magnetisation.
Q23
A material suitable for making a permanent magnet should have:
A permanent magnet must hold its magnetisation and resist being demagnetised, so both quantities must be high. Steel and alnico are typical choices.
Q24
The core of an electromagnet is made of soft iron because soft iron has:
Soft iron magnetises strongly when the current flows and loses that magnetisation almost completely when it stops, which is exactly what an electromagnet needs.
Q25
The area enclosed by a hysteresis loop represents:
The loop area is the energy dissipated as heat in each magnetisation cycle. Transformer cores are made from materials with narrow loops to keep this loss small.
Q26
Magnetisation M is defined as:
M is the net magnetic moment per unit volume of the material, with units of ampere per metre.
Q27
The three quantities B, H and M are related by:
The total field combines the applied field H and the material's own magnetisation M, giving B = μ0(H + M).
Q28
A bar magnet suspended freely in the Earth's field oscillates with a period T. If its magnetic moment is doubled, the period becomes:
The period varies as one over the square root of the magnetic moment, so doubling m divides the period by √2.
Q29
Domains in a ferromagnetic material are:
A ferromagnet is divided into domains, each with its atomic dipoles aligned. An unmagnetised sample has its domains pointing in random directions so the net moment is zero.
Q30
A compass needle placed at the Earth's magnetic pole would:
At the magnetic pole the field is vertical, so the dip is 90° and a freely suspended needle aligns with the vertical.
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All thirty questions with the formula sheet printed on the front page and ruled working space for your circuit reductions. Print it, solve it, keep it.
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