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'.
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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=LV When 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 aˉ=−meE 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=mcEτ...............(i) E=L−V...........(ii) Where τ=relaxation time between two successive collision Let n=number density of electrons in the conductor N0. 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=vdL Current I=tq =LnALe×vd =nAevd Using equation (i) and (ii), we get that I=nAe×(−mLe(−V)τ) =(mLne2Aτ)V