1. Magnetic and Electrical Fields in materials

Question 1

What is (BH)max?

Answer 1

This point occurs in the second quadrant of the B-H loop and corresponds to maximum magnetic potential energy. This translates to the highest possible B for a given volume of material. (also thought as the energy stored in the magnetic field around a magnet, and is the optimum working point for the battery)

Question 2

What is Hc?

Answer 2

Hc is the coercive force and corresponds to the field at which the material demagnetises completely.

Question 3

What is Br?

Answer 3

Br is the remanent magnetic field i.e. that when H is reduced to zero (hence can only be measured easily in long rods).

Question 4

What is Bsat?

Answer 4

Bsat is the saturation field and occurs when all the individual magnetic dipole are aligned by H. The gradient of the B-H curve is µ0 at higher fields (negligible increase compared to Bsat.).

Question 5

What is

µ?

Answer 5

µ is the permeability and is given by the gradient of the B-H curve in the linear region.

Question 6

Define the electric field E

Answer 6

The electric force per unit charge, and is a vector field, units N/C

Question 7

What does Gauss’s law state

Answer 7

The surface integral of the electric field through a surface gives you the charge enclosed

Question 8

What does Coulomb’s law state?

Answer 8

That like charges repel and opposite charges attract, with a force proportional to the product of the charges and inversely proportional to the square of the distance between them.

Question 9

What is a dielectric

Answer 9

A dielectric (or dielectric material) is an electrical insulator that can be polarized by an applied electric field.

Question 10

What are polar dielectrics

Answer 10

Dielectrics where the dipoles are permanently present but disordered

Question 11

What is polarisation

Answer 11

The contribution to the electric field from the charges between the plate of a capacitor, ie. in the dielectric.

Question 12

What is the equation for the Displacement field

Answer 12

D = ε0*E + P where P is the polarisation/electric field from charges between the plates, E - electric field

Question 13

What does the displacement field allow us to do?

Answer 13

Determine what electric field will result from the combination of the electric fields generated from charges in the capacitor and in the dielectric between the plates. It represents the free charges (as opposed to bound within the dielectric) and thus the field developed by the charges in the plates. If there is no dielectric then D = ε0*E.
In free space, the electric displacement field is equivalent to flux density, a concept that lends understanding to Gauss’s law.

Question 14

Why is the there the distinction between the B and H field

Answer 14

The H field is devised so that the magnetisation current can be removed from amperes law inside a material, as this is not possible to measure. This leaves only the conduction currents in the amperes law expression: ∇ x H = μ0 * jc (jc = conduction currents). Therefore it is the component of the megnetic field due to conduction currents. However this definition does not mean that permanent magnets with no flowing currents do not have an H field, they do.
There is no distinction between B and H outside a material as they have the simple relation B = μ0H.

Question 15

What is the equation for total H field?

Answer 15

H total = H0 + Hd
H0 = externally applied H field
Hd = H field fue to demagnetisation

Question 16

What is the magnetisation of a material?

Answer 16

The total dipole moment / Volume

Question 17

What is the equation for the torque on a dipole?

Answer 17

Torque = magnetic dipole moment x B (Magnetic field)

Question 18

What is the magnetic suscepibility

Answer 18

Measures how easily the atomic dipole moments may be rotated, thus the Magnetisation = susceptibility x H (auxilary field)

Question 19

What is the susceptability of Diamagnetic materials?

Answer 19

Susceptability < 0 (they expel magnetic field lines)

Question 20

What is the susceptability of Paramagnetic materials?

Answer 20

Suscepability > 0 (they concentrate magnetic field lines)

Question 21

Why does a sufficiently large magnetic field need to be applied to a paramagnetic material to align the dipoles?

Answer 21

As the tendency for dipoles to align with the field competes with thermal effects

Question 22

What are ferromagnets?

Answer 22

Materials which exhibit spontaneous alignment of their magnetic dipoles

Question 23

What are antiferromagnets?

Answer 23

Adjacent dipoles are oppositely directed leading to no overall magnetisation

Question 24

What are ferrimagnets?

Answer 24

where anti-ferromagnetic couplic occurs but the two dipoles have different strengths, therefore some ferromagnetic materials are actually ferrimagnets

Question 25

What is the magnetic dipole moment of aligned spins?

Answer 25

1 Bohr magneton

Question 26

What is the curie temperature?

Answer 26

the Curie temperature (TC), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, to be replaced by induced magnetism.

Question 27

What are the 3 known ferromagnetic elements at room temp?

Answer 27

Fe (bcc), Ni (fcc), Co (hcp)

Question 28

Why does smelted bbc iron not exhibit magnetisation

Answer 28

Due to the formation of domains

Question 29

How does a magnetic field affect domain sizes in bcc iron?

Answer 29

The domains that are alligned with the applied magnetic field grow in size.

Question 30

What affects the ease at which domains can grow on the application of an external magnetic field?

Answer 30

The ease at which domains grow and their walls move depends on the presence of pinning centres such as impurities, grain boundries, or other inhomegeneities in the material. Pinning causes hysteresis and loss linearly with frequency.

Question 31

Why are B-H curves measured for long rods with the field applied parallel to the rod axis?

Answer 31

So that the material can’t demagnitise itself, so H=H0 as there is no magnetising currents to generate a demagentising field Hd

Question 32

Where does BH(max) occur for linear materials?

Answer 32

At the mid-point of the second quadrant on the BH curve

Question 33

Why do permanent magnets operate in the 2nd quadrant of B-H curve?

Answer 33

As when there is no externally applied H0 field, the demagnetising field Hd is the only H field present as this is thought of as negative

Question 34

Differences between H and B fields within a magnet and at the boundary:

Answer 34

H and B fields act in opposite directions inside the magnet, and B much be continuous across the boundary.

Question 35

What aplifies the demagnetising field

Answer 35

The shape of the demagnetising field (N = demagnetising factor, N=0 for infinite cylinder (field parallel to axis, N=1 for flat plate (field perpendicular to the surface))

Question 36

What is the equation for the H field in terms of demagnetisation factor?

Answer 36

H = -NM (M= magnetisation)

Question 37

What is the permeability of a magnetic material?

Answer 37

The permeability of a material is a measure of its ability to support a magnetic field within itself. It can be thought of as the effective multiplication of an external magnetic field by the alignment of the magnetic domains within the material.