Lecture 1 - Magnetic Materials Flashcards

1
Q

Whatโ€™s the basic unit of magnetic systems (magnetostatics)?

A

The basic unit in magnetostatics is the magnetic dipole. No magnetic monopoles exist in contrast to electric monopoles, i.e. charges

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2
Q

What causes a rise of a magnetic field?

A

Moving electric charges give rise to magnetic fields

Two sources:

1) Conduction Currents: flowing electrical currents in wires
2) Bound Currents: The intrinsic magnetic moment of fundamental particles and atoms within a material [e.g. the spin of an electron]

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3
Q

What are the B-field and the H-field?

A

B-field: Magnetic Flux, Magnetic Induction or simply Magnetic Field. It has units of Tesla.

H-field: Auxiliary Field. It has units of A/m.
H_o = Externally Generated
H_d = Internally Generated (PM)

H = H_o + H_d

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4
Q

What are the relationships between the B and H fields?

A
โˆ‡x๐ = ฮผ_o*๐ฃ
โˆ‡x๐‡ = ๐ฃ_๐œ

where j : current density from both conduction and bound currents

where j_c: current density due to conduction currents

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5
Q

What is the relationship between B and H outside a material?

A

๐ = ฮผ_o*๐‡

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6
Q

When does ๐ = ฮผ_o*๐‡ apply?

A

Only outside a material, and therefore there is no distinction between B and H then.

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7
Q

How do permanent magnets exhibit fields?

A

Permanent Magnets have only bound currents so they generate an B field. However, they still exhibit an H field through B=ฮผฮฟฮ—. We label the self-generated field by H_d

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8
Q

What is a magnetic dipole moment?

A

Itโ€™s the basic parameter in describing the generation of fields in materials.
๐ฆ = I๐€ where A the cross-sectional area of a loop.

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9
Q

Torque on a magnetic dipole?

A

๐ญ๐š๐ฎ=๐ฆx๐

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10
Q

What is Magnetisation?

A

The total dipole moment in a material divided by itโ€™s volume

M = Sum{i.ฮดฮ‘}/V

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11
Q

What are the contributions affecting the net magnetic field B?

A

1) Magnetisation of the material
2) An externally imposed field

๐ = ฮผ_o*(๐‡+๐Œ)

Many Caveats:
H depends on M as demagnetisation effects give rise to H_d, opposing H_o.

M depends on B -> the bigger the field B, the bigger the torque, the greater the alignment. If M becomes constant -> spins are fully aligned for all B โ€“ Ideal Permanent Magnet.

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12
Q

What is magnetic susceptibility? What quantities does it relate?

A

A material property that measures how easily the atomic dipole moments may be rotated.

Symbolised by ฯ‡ or ฯ‡_m and following
ฯ‡+1 = ฮผ_r.

Relates ๐Œ=ฯ‡๐‡

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13
Q

Get from ๐ = ฮผ_o*(๐‡+๐Œ) to ๐=ฮผ๐‡

A

๐ = ฮผ_o*(๐‡+๐Œ)

1) ๐Œ=ฯ‡๐‡
2) ฯ‡+1 = ฮผ_r

=> ๐ = ฮผ_o(๐‡+ฯ‡๐‡) (using 1)
=> ๐ = ฮผ_o
๐‡(1+ฯ‡)
=> ๐ = ฮผ_o๐‡ฮผ_r (using 2)
=> ๐ = ฮผ๐‡

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14
Q

What are Diamagnetic materials?

A

Diamagnetic materials have ฯ‡<0 and thus appear to expel magnetic field lines.

The magnetic response arises from the interaction between the applied magnetic field and pairs of electrons. The magnetic field affects the two differently orientated spin electrons in a different way such that a small oppositely directed magnetic field is induced. As a consequence, diamagnetic materials are repelled by PM.

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15
Q

What are Paramagnetic materials?

A

Paramagnetic materials have ฯ‡>0 and thus appear to concentrate magnetic field lines.

The magnetic response is dominated by the influence of unpaired spins in electron shells. The induced magnetic field is as such in the same direction as the applied field.

A sufficiently large external field that overcomes thermal effects is needed to cause this alignment.

โ† โ†‘ โ†’ โ†“ โ†’ โ†’ โ†’ โ†’
โ†’ โ†“ โ† โ†‘ โ†’ โ†’ โ†’ โ†’
โ†’ โ†“ โ† โ†‘ โ†’ โ†’ โ†’ โ†’
โ† โ†‘ โ† โ†‘ โ†’ โ†’ โ†’ โ†’

H = 0 H applied โ†’

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16
Q

What are ferromagnetic materials?

A

Ferromagnets are materials which exhibit spontaneous alignment between magnetic dipoles. (Origin of alignment is quantum mechanical โ€“ exchange interaction).
They can have ฮผ_r of the order of 10^6.
They can exhibit large magnetisation without external fields and thus act as permanent magnets.

โ† โ†‘ โ†’ โ†“                   โ†’ โ†’ โ†’ โ†’
โ†’ โ†“ โ† โ†‘                   โ†’ โ†’ โ†’ โ†’
โ†’ โ†“ โ† โ†‘                   โ†’ โ†’ โ†’ โ†’ 
โ† โ†‘ โ† โ†‘                   โ†’ โ†’ โ†’ โ†’ 
  t = 0                        t = 5 

5 is random

17
Q

What are antiferromagnets?

A

Antiferromagnets are materials which have adjacent dipoles that are oppositely directed from spontaneous alignment, leading to no overall mangetisation.

                     โ†“ โ†‘ โ†“ โ†‘                 
                     โ†‘ โ†“ โ†‘ โ†“                 
                     โ†“ โ†‘ โ†“ โ†‘ 
                     โ†‘ โ†“ โ†‘ โ†“
18
Q

What are ferrimagnets?

A

They have adjacent dipoles oppositely spontaneously from exchange interaction but the two dipoles have different strengths and thus they exhibit some magnetic interaction like ferromagnets.