Magnetism

Origin of Magnetism
An accelerated charge produces a magnetic field around it. In an atom, there are electrons revolving around the nucleus , generating magnetic field. At the same time, the electrons also spin about their own axis , producing more net magnetic field. If in an orbital, there are two electrons with anti-parallel spins , then the magnetic moments are cancelled. In a half - filled orbital, the magnetic moments are not cancelled and hence there is a net magnetic moment.

Magnetic Pole Strength
Pole Strength (m) has the unit A.

Magnetic Dipole Moment
M = m.2l

S/i unit : Am

M = nIA

Magnetic Induction
B= ( µ0 /4 π ) ( m 1/ r 2)

(a) Point situated on the axial line (End-on position):-

F = (µ0/4π) [2Mr/(r2-l2)2]

In case of a magnetic-dipole, F = (µ0/4π) [2M/r3]

(b) Point situated on equatorial line (Broad side-on position)

F = (µ0/4π) [M/(r2+l2)3/2]

In case of a magnetic-dipole, F = (µ0/4π) [M/r3]

(c) Point situated anywhere:-

F= (µ0/4π) [M/r3] √1+3 cos2θ

Direction, tan β = ½ tan θ

Torque
T = MBsinθ

Potential Energy = U = - MBcosθ

W =  MB  (cos θ1  – cos θ2 )

Bar Magnets
Force between bar magnets with like poles facing each other

F = μ0/4π  6MM'/ d4

The Magnetic Lines of Force inside a bar magnet is from South to North pole.

When two bar magnets are lying mutually perpendicular to each other,

then, M = √[M12+M22] = √2 mpI

Revolving Electron
The ratio of magnetic dipole moment with angular momentum of revolving electron is called as gyromagnetic ratio.

Gyromagnetic Ratio = M/L = 8.8 x 1010C / kg

magnetic moment = M = evr / 2

Magnetic Intensity
Magnetic Intensity (H) is a quantity used in describing magnetic field strength of a field.

Magnetization
The net magnetic dipole moment per unit volume is called as Magnetization (Mz).

Domain Theory
The region in which all the magnetic moments are aligned in the same direction are known as domains.

Diamagnetism
Silver, lead , silicon , nitrogen , sodium chloride , copper , antimony , gold , mercury , water , air , hydrogen , etc.

1) All the orbitals are completely filled.

2) The spins are paired and the magnetic field is repelled . The diamagnetic materials move away from stronger magnetic field to weaker magnetic field.

3) If a thin rod of diamagnetic substance is freely suspended in external magnetic field, it comes to rest with it's length perpendicular to the field.

4) In absence of external magnetic field, the net magnetic moment is zero.

Paramagnetism
Aluminium, Manganese , Chromium , Platinum , oxygen , sodium , calcium , lithium , copper chloride , tungsten , niobium , etc.

1) Atom contains unpaired electron ; i.e. their orbitals are not completely filled.

2) The spins do not cancel each other and the magnetic field is attracted . The paramagnetic materials move towards the stronger magnetic field.

3) If a thin rod of paramagnetic substance is suspended freely in a magnetic field, it comes to rest , parallel to the magnetic field.

4) In absence of external magnetic field, the dipole moments of atoms are randomly oriented , and hence the net dipole moment is zero.

Ferromagnetism
1) Atom contains a large number of unpaired electrons, which results in large magnetic moment.

2) The ferromagnetic materials move towards the stronger magnetic field.

3) When ferromagnetic substances are kept in magnetic field, they get strongly magnetized in the direction of magnetic field.

4) In the absence of external magnetic field, these materials have a resultant magnetic moment.

Curie Temperature
The temperature at which the domain structure is destroyed and the ferromagnetic substance loses its magnetism, is called Curie Temperature. Above Curie temperature, ferromagnetic substances become paramagnetic.

Curie Law
Magnetic susceptibility is inversely proportional to temperature.