Magnetism and matter

 1. Magnetic Dipole Moment of a Current Loop and Revolving Electron

Magnetic dipole moment of a magnet is given as , M = m 2l, where m is pole strength, 2l is separation between poles. Its SI unit is ampere (metre)2 abbreviated as Am2. Magnetic dipole moment of a current loop is

M = NIA

The direction of M is perpendicular of the plane of loop and given by right hand thumb rule.

Magnetic dipole moment of a revolving electron

= IA =ev2πr×πr2=evr2

where n is frequency, r is radius of orbit

M=e2meLampm2

where L = mevr is angular momentum of revolving electron.

2. Magnetic Field Intensity due to a Magnetic Dipole

Magnetic field intensity at a general point having polar coordinates (r, θ) due to a short magnet is given by

B=μ04πMr31+3cos2θ−−−−−−−−−√

where M is the magnetic moment of the magnet.

Special Cases

(i) At axial point θ = 0,

Baxis=μ04π2Mr3

(ii) At equatorial point θ = 90°

Beqt.=μ04πMr3

3. Gauss’s law in magnetism

The net magnetic flux through any closed surface is zero.

∮B⃗ .ds→=0

4. Earth’s Magnetism

The earth’s magnetic field may be approximated by a magnetic dipole lying at the centre of earth such that the magnetic north pole Nm is near geographical north pole Ng and its magnetic south pole Sm is near geographical south pole Sg. In reality, the north magnetic pole behaves like the south pole of a bar magnet inside the earth and vice versa. The magnitude of earth&aposs magnetic field at earth&aposs surface is about 4×10–5 T.

4. Elements of Earths&apos Magnetic Field

Earth’s magnetic field may be specified completely by three quantities called the elements of earth&aposs magnetic field. These quantities are

(i) Angle of declination (a): It is the angle between geographical meridian and the magnetic meridian planes.

(ii) Angle of dip (θ) : It is the angle made by resultant magnetic field Be with the horizontal. The angle of dip is 0° at magnetic equator and 90° at magnetic poles. Angle of dip is measured by Dip circle. It is also called as magnetic inclination

(iii) Horizontal component (H) of earth&aposs magnetic field (Be)

H = Be cos q …(i)

Vertical component of Be is V = Be sin q …(ii)

∴ Be=H2+V2−−−−−−−√ …(iii)

and tan θ=VH …(iv)

5. Important Terms in Magnetism

(i) Magnetic permeability (µ): It is the ability of a material to allow magnetic lines of force to pass through it and is equal to μ=BH, where B is the magnetic field strength and H is the magnetic field intensity.

The relative magnetic permeability μr=BB0=μμ0

where µ0 is the permeability of free space and B0 is the magnetic field strength in vacuum.

(ii) Intensity of magnetisation (M⃗ ): It is defined as the magnetic moment per unit volume of a magnetised material. Its unit is Am^–1

i.e., M⃗ =m⃗ V

(iii) Magnetising field intensity (H): It is the magnetic field used for magnetisation of a material. If I is the current in the solenoid, then magnetising field intensity H=nI, where n = number of turns per metre. Its unit is Am^–1

(iv) Magnetic susceptibility: It is defined as the intensity of magnetisation per unit magnetising field, i.e.,

χm=MH

It has no unit.

It measures the ability of a substance to take up magnetisation when placed in a magnetic field.

7. Classification of Magnetic Materials

Magnetic materials may be classified into three categories :

(i) Diamagnetic substances: These are the substances in which feeble magnetism is produced in a direction opposite to the applied magnetic field. These substances are repelled by a strong magnet. These substances have small negative values of susceptibility χ and positive low value of relative permeability µr, i.e.,

–1≤χm<0and0≤μr<1

The examples of diamagnetic substances are bismuth, antimony, copper, lead, water, nitrogen (at STP) and sodium chloride.

(ii) Paramagnetic substances: These are the substances in which feeble magnetism is induced in the same direction as the applied magnetic field. These are feebly attracted by a strong magnet. These substances have small positive values of M and χ and relative permeability µr greater than 1, i.e.,

0<χm<ε,1<μr<1+ε

where ε is a small positive number. The examples of paramagnetic substances are platinum, aluminium, calcium, manganese, oxygen (at STP) and copper chloride.

(iii) Ferromagnetic substances: These are the substances in which a strong magnetism is produced in the same direction as the applied magnetic field. These are strongly attracted by a magnet. These substances are characterised by large positive values of M and χ and values of µr much greater than 1, eg., Iron, cobalt, nickel and alloy like alnico.

i.e. χm>>1,μr>>1

8. Curie Law

It states that the magnetic susceptibility of paramagnetic substances is inversely proportional to absolute temperature, i.e.,

χm∝1T⇒χ=CTwhere C is called Curie constant

9. Curie Temperature

When temperature is increased continuously, the magnetic susceptibility of ferromagnetic substances decrease and at a stage the substance changes to paramagnetic. The temperature of transition at which a ferromagnetic substance changes to paramagnetic is called Curie temperature. It is denoted by TC . It is different for different materials. In paramagnetic phase the susceptibility is given by

χm=CT–TC

10. Diamagnetism is universal properties of all substances but it is weak in para and ferromagnetic substances and hence difficult to detect.

11. Electromagnets and Permanent Magnets

Electromagnets are made of soft iron which is characterised by low retentivity, low coercivity and high permeability. The hysteresis curve must be narrow. The energy dissipated in magnetisation and demagnetisation is consequently small.

Permanent magnets are made of steel which is characterised by high retentivity, high permeability and high coercivity.

They can retain their attractive property for a long period of time at room temperatures.