Question

The motion of electron inside a current carrying conductor is

Answer 1

Free Electrons inside a current carrying conductor moves randomly unless they attached to a Battery.

As soon as we attached battery to Current Carrying Conductor, Electrons start moving from Negative Terminal to Positive Terminal of Battery.

This happens due to potential difference applied by battery which causes EMF (Electro Motive Force) in conductor.

EMF drag electrons to one direction from other, this forms electric current in conductor.

So Motion of Electrons inside a conductor is Current.

Answer 2

Answer:

The electrons moves with drift velocity (v™) with random direction change due to collisions inside the conductor.

Explanation:

Equation of Motion of Electron Electric Field :

If the electric field is E and electrons having charge e and mass m moves with a velocity v;

$m \frac{dv}{dt} = e.E \: ...equation(1)$

Hence according to equation (1) there will be a constant acceleration acting on electrons. Then;

1. Velocity of electrons will be nearly equal to speed of light (c), this is a relativistic case where mass converts into energy.
2. Any charged particles having acceleration radiates energy according to Maxwell's EM radiation.*

(* When any change is accelerated, the kinetic energy must translate into radiation else the charge must grow in mass that isn't possible)

But In Practical; there are so many resistive forces also present in conductors:

1. Electron-electron collisions
2. Vibration of atom's nucleus
3. Impurities of metarials
4. Different ions
5. Phonon interaction

So we can say resistive force (Fr) ;

$Fr \propto velocity(v) \\ Fr = kv \\Fr = \frac{mv}{ \tau} \: (\tau = constant)$

So, now Equation of Motion;

$m \frac{dv}{dt} = eE - \frac{mv}{ \tau} \: ...equation(2)$

Hence, due to the resistive force the velocity of electrons will be Uniform (Terminal velocity);

Let terminal velocity = v™

Therefore:

$|m \frac{dv}{dt} | (at \: terminal \: velocity) = 0 \\ so \: \: m \frac{dv™}{dt} = 0$

Hence we get;

$\frac{mv™}{ \tau} = eE \\ or \: v™ = (\frac{ E \: e}{m}) \: \tau \: ...equation(3)$

τ = relaxation time between two collisions = constant

v™ = Drift velocity of electrons

Random motion of electrons due to collisions is shown in figure .

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