Lorentz and Drude theory, Drift speed of electron

INTRODUCTION TO ELECTRICITY

ELECTRICITY: Electricity is a branch of physics which deals with study of charges. The property of matter that is responsible for electrical phenomena is called charge.

Electricity is further divided into two sub branches. They are:

1)    Static electricity: the study of charges which are at rest.

And

2)    Current electricity: study of charges under motion. This is what we are also calling as electric current.

In terms of electric current materials are classified into three types:

1)    Conductors: the materials which can able to allow electric current to pass through them. Eg: all metals, water with salts and minerals, etc.

2)    Insulators: the materials which cannot able to allow electric current to pass through them. Eg: wood, plastic, rubber, etc.

3)    Semi conductors: the materials which cannot allow electric current freely as conductors. These materials can able to allow only a partial current to flow slowly through them. Eg: silicon, germanium, L.E.D, etc

 

Lorentz and Drude theory:

  Drude and Lorentz, scientists of the 19th century, proposed that conductors like metals contain a large number of free electrons while the positive ions are fixed in their locations. The arrangement of the positive ions is called lattice.

Let us understand the behaviour of electrons in lattice space. Assume that a conductor is an open circuit. The electrons move randomly in lattice space of a conductor as shown in figure. When the electrons are in random motion, they can move in any direction. Hence, if you imagine any cross section as shown in figure, the number of electrons, crossing the cross section of a conductor from left to right in one second is equal to that of electrons passing the cross section from right to left in one second. It means that net charge moving along a conductor through any cross section is zero when the conductor is in open circuit.

     When the ends of the conductor are connected to the battery through a bulb, the bulb glows because energy transfer takes place from battery to the bulb.

The electrons are responsible for this transfer of energy. If the electrons are responsible for transfer of energy from battery to bulb, they must have an ordered motion. When the electrons are in ordered motion, there will be a net charge crossing through any cross section of the conductor. This ordered motion of electrons is called electric current.

                                                                        

Let us define electric current quantitatively,

 

Electric current is defined as the amount of charge crossing any cross section of the conductor in one second.

Let Q be the charge crossing through any cross section of the conductor in a time interval t. Then the amount of charge crossing through that cross section in one second is Q/t. Therefore,

Electric current = electric charge/time interval

I = Q/t

The SI unit of electric current is ampere denoted by A.

1 Ampere = 1 Coloumb/1 Second

1 A = 1 C/s

 

What causes the electrons to set in ordered motion?

 

When a conductor is connected to a battery in a closed circuit, then immediately an electric field is set up throughout the circuit which makes electrons to accelerate in ordered motion.

  During this motion,

 

i)                    each electron is attracted to a nearby lattice ion and collides with it.

ii)                During collision the energy of the electron is released in the form of heat.

iii)              The electron comes to a temporary halt.

iv)              Then this electron is once again accelerated by electric field.

v)                Then electron again moves and collides with next lattice ion, releases energy and comes to halt. Again field accelerates electron.

vi)              Like this an electron continuously collides with lattice ions during its motion.

vii)           The same process is applied for all the electrons in the circuit.

 

NOTE: The direction of electric field is opposite to the direction of electron.

 We have two types of currents during the flow of electron in a circuit.

ELECTRONIC CURRENT: The current produced in the direction of flow of electron is called electronic current.

CONVENTIONAL CURRENT: The current produced in opposite direction to the direction of electron is called conventional current.

 We consider the direction of current as the direction of conventional current because an electron flows from low potential to high potential. So, conventional current flows from high potential to low potential.

Drift speed of electron:

Consider a conductor with cross sectional area A. Assume that the ends of the conductor are connected to a battery to make the current flow through it. Let v_d be the drift speed of the charges and n be the number of charges present in the conductor in an unit volume (charge density). The distance covered by each charge in one second is v_d. Then the volume of the conductor for this distance is equal to Av_d . The number of charges contained in that volume is equal to nAv_d. Let q be the charge of each carrier. Then the total charge crossing the cross sectional area at position D in one second is nqAv_d. This is equal to electric current.

Hence,

Electric current I = nqAv_d ………………. (1)

Therefore, v_d = I/nqA ………………. (2)

We know that the charge carriers in a conductor are electrons. The magnitude of electric charge ‘e’ is 1.602 x 10^-19C.

Let us calculate the drift speed of electron in a copper wire carrying a current of 1A and cross sectional area A = 10^-6 m². The electron density of copper that was found experimentally is n = 8.5x10²⁸m^–3. Substituting these values in equation (2) with q = e, we get,

v_d = 1/(8.5x10²⁸x10^-6x1.6x10^-19)

v_d = 7x10^-5m/s = 0.07mm/s

This shows that the electrons are moving very slowly.

 Why does a bulb glow immediately when we switch on?

When we switch on any electric circuit, irrespective of length of the connecting wire (conductor) an electric field is set up throughout the conductor instantaneously due to the potential difference of the source (battery) connected to the circuit. This electric field makes all the electrons to move in a specified direction simultaneously.

thank you