Mobility of electron (u_e) is defined as the drift velocity of electron per unit electric field applied.

u_e= drift velocity/electric field= V_d/E

Thus                                 V_d=u_eE

The  SI unit of mobility is m²s^-1V^-1 or ms^-1N^-1C

As  by the relation of the current and drift velocity (already discussed)

I=Anev_d (1)

By putting value of v_d in above equation we get

I=Aneu_eE

OHM’S LAW

Statement:– Ohm’s law states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) across the ends of the conductor,provided physical conditions of the conductors such as temperature,mechanical strain etc. Are kept constant i.e. IαV

Or                                                   VαI or V= RI

Or                                                   V/I=R=a constant

Where R is known as resistance of the conductor . It depends upon the length ,shape and the nature of the material of the conductor. The variation between potential difference (V) and current (I) through a conductor is a straight line.

Deduction of Ohm’s Law:

As drift velocity is given by V_d=eEt/m

But                         Electric field across the conductor of length l is

E=V/l

Thus                              V_d=e V/ml

Also,                              I=Anev_d

By putting value of v_d in the equation of I (equation 1 of relation of the current and drift velocity),we get

I=Ane(eV/ml)=(Ane²/ml)V

Or                        V/I=ml/Ane²=R

Where R is a constant for a given conductor. It is known as the resistance of the conductor.

Thus                                  V=RI

This  is Ohm’s law.

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Therefore, the volume of the conductor = Al

If n is the number of free electrons per unit volume of the conductor, then the total number of free electrons in the conductor=A/n.

If e is the charge on each electron then total charge on all the free electrons in the conductor

Q=A/ne                                     (1)

Let a constant potential differences V is applied across the ends of the conductor with the help of a battery

The electric field set up across the conductor is given by

E=V/l

Due to this field, the free electrons present in the conductor will begin to move with a drift velocity v_d towards the left hand side of the conductor.

Thus the time taken by the free electrons to cross the conductor is

t=l/v_d (2)

As current I=q/t                                                     (3)

By substituting equation (1) and (2) in equation (3),

We get

I=Alne/l/v_d

Or                                      I=Anev_d (4)

Since A,n and e are constant

I∞v_d

Hence the current flowing through a conductor is directly proportional to the drift velocity.

Explanation and Example. In a conductor, there are large number of free electrons. When we close the circuit, the electric field is established in the circuit with the speed of electromagnetic wave which causes electron drift at every portion of the circuit. Due to which the current is set up in the entire circuit instantly. The current thus set up does not wait for the electrons to flow from one end of the conductor to another end. It is due to this reason, the electric bulb glows immediately when the switch is on.

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Coercivity is defined as the value of the magnetising field at which the intensity of magnetisation becomes zero. It is also known as coercive field.

Hence, the coercivity of a material is a measure of the strength of the reverse magnetising field required to finish out the residual magnetism of the magnetic material.

Reference: This article is referred from my authored book “electrical engineering materials” having ISBN 978-81-272-5491-9. In case of any doubt, then comment it.

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The magnetism remaining in the magnetic material, even when the magnetising field is reduced to zero is called residual magnetism. The power of retaining this magnetism is called the retentivity or remanence.

Therefore, the retentivity is also defined as the measure of the magnetisation remaining in the material when the field is totally removed.

Reference: This article is referred from my authored book “electrical engineering materials” having ISBN 978-81-272-5491-9. In case of any doubt, then comment it.

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Soft magnetic materials have low retentivity and low coercivity. These are those materials which have high initial permeability, low hysterisis loss and large magnetic induction. These materials can be easily magnetised and demagnetised. Therefore, these are known as soft magnetic materials.

Reference: This article is referred from my authored book “electrical engineering materials” having ISBN 978-81-272-5491-9. In case of any doubt, then comment it.

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Ferrimagnetic materials commonly known as ferrites, can be generally represented by chemical formula XOFe₂O₃,

where X stands for Mn, Co, Ni, Cu, Mg, Zn, Cd etc.

If X is Fe, then compound is Fe₃O₄.

X-ray crystallography proves that ferrites are usually crystals and have a spine structure.

Reference: This article is referred from my book “electrical engineering materials” having ISBN 978-81-272-5069-0. In case of any doubt, comment it or post it.

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Ferrites have following applications:

• Ferrites have importance in engineering and technology because they possess spontaneous magnetic moment below the Curie temperature just as iron, cobalt, nickel.
• Due to vey low eddy current losses, ferrites are used as a core of coils in microwave frequency devices and computer memory core elements.
• Due to relatively low permeability and flux density compared to iron, ferrites are not suitable for the use in high field and high power applications, such as motors, generators and power transformers, but they can be used in low field and low power applications.
• Ferrites are used as ferromagnetic insulators in electrical circuits.
• Ferrites like ZnO find low frequency applications in timers. They are also used as switches in refrigerators, air conditioners, etc.
• Ferrites are used as magnetic head transducer in recording.

Reference: This article is referred from my book “electrical engineering materials” having ISBN 978-81-272-5069-0. In case of any doubt, comment it or post it.

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Hard magnetic materials are those which have high coercivity, high retentivity and low loss in magnetisation due to mechanical treatment and no effect of temperature. These materials are called hard because these are difficult to magnetise and demagnetise. The higher the value of coercive force the harder is the magnetic material.

Example: The strength of the reverse magnetic field that is coercivity needed to completely demagnetise steel is more than that required for iron.

Reference: This article is referred from my book “electrical engineering materials” having ISBN 978-81-272-5069-0

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In case of polycrystalline solids, the various crystals in a polycrystals are randomly oriented, so that properties are same in all directions. However if specific treatment such as cold rolling is given to certain polycrystalline substances, then magnetic properties become different in different directions. This anisotropy produced in the material is called induced anisotropy.

This property is of practical importance.

Example: thin films of Ni-Fe alloy deposited on to a substrate by evaporation in vacuum with magnetic field applied in the plane of the substrate show spontaneous magnetisation in the direction of the applied field. These magnetic films are used as storage devices in computers.

Reference: This article is referred from my book “electrical engineering materials” having ISBN 978-81-272-5069-0

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Magnetic anisotropy is that property due to which ferromagnets tend to magnetize along certain crystallographic axes, called directions of easy magnetization.

Example: In certain single crystals such as iron.

The magnetic properties depend upon the direction in which these are measured.

In case of iron, there are six preferred directions of spontaneous magnetisation.

In case of iron

Reference: This article is referred from my book “electrical engineering materials” having ISBN 978-81-272-5069-0

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