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 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 1010 C / 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 .

 Iron
 Nickel
 Gadolinium
 Fe2O3 | 893

Above Curie temperature , ferromagnetic substances become paramagnetic .

## Curie Law

Magnetic susceptibility is inversely proportional to temperature .