MAGNETISM AND MATTER

Bar Magnet

Bar Magnet

• It has 2 equal and opposite poles

• When freely suspended, it orients itself along the geographic north and south

• When a bar magnet is cut into 2 pieces, it forms 2 magnets with the north and south pole

• There is no magnetic monopole (isolated poles cannot exist)

• When a bar magnet is cut laterally, its pole strength decreases and when it is cut transversely its pole strength remains the same

Magnetic Moment

m = NIA

m = p x l (p-pole strength,l=length)

Magnetic Field Lines

Imaginary lines that represent the magnetic field around a magnet

Properties of Magnetic Field Lines

• They form continuous curves that originate from the north pole and ends at south pole outside and it goes from south pole to north pole inside

• They never intersect

• They are closer together in areas of stronger magnetic field and spread out in areas of weaker magnetic field

• The density of magnetic field lines is proportional to the strength of the magnetic field (greater the number of field lines per unit area, stronger the magnetic field)

• If the magnetic field lines are parallel, then the magnetic field is uniform

• The direction of the magnetic field is given by the tangent to the field lines at that point

Magnetic field due to a Bar Magnet as a Solenoid

At an axial point,

B = (µₒ/4π)(2m/r³)

At an equatorial point,

B = (-µₒ/4π)(m/r³)

Dipole in a uniform magnetic field

𝜏 = mxB = mbsinθ

U = -m.B = mbcosθ

Special Cases:

1. If  θ = 0º:

   • 𝜏 = 0

   • U = -mB

   • Stable

2. If  θ = 90º:

   • 𝜏 = mb

   • U = 0

3. If  θ = 180º:

   • 𝜏 = 0

   • U = mb

   • Unstable

Dipole Analogy of Electrostatics vs Magnetism

Gauss Law for Magnetism

The closed integral of the magnetic field over a surface is zero

∲B.dA = 0

This indicates the non-existence of magnetic monopoles

The net magnetic flux through any closed surface is zero

Magnetisation (M)

Net magnetic moment acquired by a sample per unit volume when it is placed in a magnetic field

M = mnet/V

Magnetic Field Intensity (H)

It is defined as the ratio of magnetic field induction to the permeability of the medium

H = B/µ

In a solenoid,

H=nI

Unit - A/m

Relation between B, H and M

Bₘ = µₒM

B = µₒ(H+M)

B = µH

Magnetic Susceptibility (χ)

It is the ratio of magnetisation to the magnetic field intensity

χ = M/H

Magnetic Permeability

The ability of a material to become magnetised

µᵣ = 1+χ

µ = µᵣµₒ

µᵣ (relative permeability - the ratio of permeability of medium to the permeability of free space)

Classification of Materials

1. Diamagnetic

2. Paramagnetic

3. Ferromagnetic

Diamagnetic Materials

• These materials exhibit negative magnetization, i.e., the molecules align opposite the aligned magnetic field.

• Diamagnetic materials have filled orbitals.

• They have negative susceptibility: χ < 0

  • Since χ < 0, M is opposite to H.

• The relative permeability of diamagnetic substances μr < 1.

  • μ < μ₀.

• When a diamagnetic material can move in an external magnetic field, it goes from stronger to weaker regions.

• When a diamagnetic material is placed in an external magnetic field and cannot move, the field lines expel out of it.

• A diamagnetic material will be weakly repelled in the presence of an external field.

• Superconducting materials (materials that offer 0 resistance) have their susceptibility as -1, then B will be 0. Hence superconductors are diamagnetic and repel all magnetic field lines out of it.

• Examples: Bismouth, Cu, Pb, N₂, Si, H₂O, NaCl.

Paramagnetic Materials

• In the presence of an external field, the molecules orient themselves along the direction of the field.

• They tend to move from weaker to stronger regions of the magnetic field.

• They are very weakly attracted when placed in a magnetic field.

• The magnetic field lines will pass through (converge/concentrate) a paramagnetic material.

• The susceptibility of the paramagnet is greater than zero: χ > 0
  μr > 1
  μ > μ₀

• As temperature increases, the molecules have thermal agitation, so their net magnetic moment decreases. Hence, the susceptibility of a paramagnet depends on temperature.
  χ ∝ 1/T (For paramagnets)

• Examples: Al, Na, Ca, O₂, CuCl₂

Ferromagnetic Materials

• Ferromagnetic materials are paramagnets and they form domains.

• Domains are groups of atoms/molecules that behave as a single unit.

• The susceptibility of ferromagnetic materials is very high:
  χ ≫ 0
  μr ≫ 1
  μ ≫ μ₀

• As temperature increases, the domains will break, and the ferromagnet becomes a paramagnet.

• Ferromagnets are classified as:

  • Hard Ferromagnet: Retain magnetic property even after removing from the external field.

  • Soft Ferromagnet: Does not retain the magnetic property.

• Examples:

  • Hard Ferromagnet: Alnico (Alloy), Loadstone

  • Soft Ferromagnet: Fe, Ni, Co, Gadolinium