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What are Free Electrons? What is the Formula for Drift Velocity and Current Density?
Free electron: The attractive force of the nucleus on the electrons of the outermost orbit is negligibly small in atoms of metals like silver, copper, aluminium etc. So, these electrons can be detached very easily from the atom. For example, at the room temperature, these electrons can be detached very easily from the atoms. These electrons are called free electrons. They are called ‘free’ because they can move freely within the lattice sites of the metals. Of course, they cannot move out of the atom on their own.
Drift: If a potential difference is applied between the two ends of a piece of metal, the free electrons of the metal are attracted towards the positive potential. So their motion is unidirectional. This unidirectional motion from lower potential to higher potential is called the drift of the free electrons. Due to this drift, a current flows through the metal; these free electrons are then called the charge carriers.
Metals contain a large number of free electrons. So, current flows through them. Hence, metals are generally good conductors of electricity. On the other hand, at ordinary temperatures, there are no free electrons in wood, paper, rubber, etc.; so they are insulators.
Origin Of resistance: Conductivity of metals is due to the drift of free electrons but no such drift occurs to atoms or ions which are comparatively heavy. They vibrate about their equilibrium positions. Free electrons, in course of their motion, collide with the vibrating atoms and ions, and are retarded. So their drift is hindered. This gives rise to the resistance. With increase of temperature vibrations of the ions increase.
So the free electrons encounter greater resistance during their drift i.e., resistance of the conductors increases. On the other hand, when the temperature reaches absolute zero, the ions come almost to a standstill. Then the free electrons can move through the empty space surrounding the ions almost without any resistance. Under this condition some metals exhibit the property of super-conductivity.
Other than metals, gas under low pressure, electrolyte, semicon-ductor also conduct current. The charge carriers in these cases are different in nature. So electric conductivity for these sub-stances cannot be explained with the free electron theory.
Drift Velocity of Free Electrons and Electric Current Density
Drift velocity of free electrons: The average velocity with which the free electrons move in a current carrying metallic wire is called drift velocity of the free electrons.
Calculation: Consider a metallic wire [Fig.],
n = number of electrons per unit volume = number density of free electrons
e = charge of an electron = 1.6 × 10-19C = 4.8 × 10-10 esu of charge
A = cross sectional area of the wire
I = electric current through the wire
vd = drift velocity of the free electrons
The number of free electrons passing through a definite cross section of the wire per second is confined within a cylinder of length vd.
Volume of that cylinder = Avd
Number of electrons in the cylinder = nAvd
So, the amount of electric charge in the cylinder = neAvd i.e., neAvd is the amount of charge that crosses any section of the wire per second. By definition, electric current is the rate of flow of electric charge across any section of a wire.
Again, electric current flowing through unit cross sectional area is called electric current density, expressed as
j = \(\frac{I}{A}\) = nevd …… (2)
It is a vector quantity.
Definition: The electric current per cross sectional area at a given point in space is termed as electric current density. It is directed along the motion of the charges.
Velocity of electric current: The velocity with which an electric field propagates through a conductor is called the velocity of electric current. This is also the velocity of propaga-tion of electrical energy.
We intuitively know that this velocity is very high. If a switch is on in a power generating station, almost instantaneously a large area is flooded with light. Actually, the velocity of electric current is equal to the velocity of light i.e., 186000 m ᐧ s-1 or 300000 km ᐧ s-1.
Comparison Of the two velocities: Remember that electric current flows due to the drift of the free electrons. But drift velocity and the velocity of electric current are vastly differ-ent ideas. Suppose, for a wire, A = 1 mm2 = 10-6 m2, n = 5 × 1028 m-3 and I = 1 A. So from equation (1), the drift velocity vd = \(\frac{1}{8000}\) m ᐧ s-1 = \(\frac{1}{80}\) cm ᐧ s-1 i.e., the electrons move through a distance of only 1 cm in 80 s . This shows how negligibly small the drift velocity is compared with the velocity of electric current.