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Question:

Explain the term 'drift velocity' of electrons in a conductor. Hence obtain the expression for the current through a conductor in terms of 'drift velocity'.

Solution:

The average velocity of all the free electrons in the conductor is called the drift velocity of free electrons of the conductor. When a conductor is connected to a source of emf an electric field is established in the conductor, such that E=V/L where V= potential difference across the conductor and L=length of the conductor. The electric field exerts an electrostatics force '-Ee' on each free electron in the conductor. The acceleration of each electron is given by a=-eE/m where, e=electric charge on the electron and m=mass of electron. Acceleration and electric field are in opposite directions, so the electrons attain a velocity in addition to thermal velocity in the direction opposite to that of electric field. vd=-eE/mτ.. (i) E=-V/L.. (ii) Where τ=relaxation time between two successive collision. Let n=number density of electrons in the conductor. No. of free electrons in the conductor =nAL. Total charge on the conductor ,q=nALe. Time taken by this charge to cover the length L of the conductor, t=L/vd. Current I=q/t=nALe/(L/vd)=nAevd. Using equation (i) and (ii), we get that I=nA e × (-e(-V)/mLτ) = (ne²Am/Lτ)V