Question

write the expression for the drift velocity of charge carriers in a conductor of length L across which a potential difference v is applied

Answer 1

We know that i = n × Vd × e × A --- ( i )
Where
n = electron density
Vd = Drift speed
e = Charge on Electron ( charge carriers )
A = Area of cross section of conductor of length L

i = V / R ---> By Ohms law , Also R = l × @ / A
where V = potential difference , R = Resistance of a consuctor , l = length of a conductor , @ = Resistivity

Thus i = V / ( l × @ / A ) = ( V × A ) / l × @
=> i = V × A / l × @
Putting the above value of i in equation ( i ) we get ,
V × A / l × @ = n × Vd × e × A
On dividing both sides by ' A ' we get
V / l × @ = n × Vd × e
=> Vd = V / l × @ × e × n is the required expression...

Answer 2

Answer:

Drift velocity =  $\frac{\sigma v}{neL}$

Explanation:

• Drift Velocity: Drift velocity is the average velocity of electrons inside a conductor when an electric field is applied to the conductor.
• Derivation:
• Suppose the cross sectional area of the cylindrical conductor = A.

        The number of electrons = n and charge of each electron = n. Total charge = ne.

Drift velocity = v,

that means in unit time the electrons cross the length v .

Volume crossed by electrons per unit time = v × A.

 Total charge crossing the volum per unit time =  V × A × ne = neAv

As we know current = total charge flow per unit time.

  So, I = neAv

• Now current density, J = $\frac{I}{A}$ = $\frac{neAv}{A}$ = nev

• If the length of the conductor is 'L' and 'V' voltage is applied across the ends, then generated electric field, E = $\frac{V}{L}$
• From Ohm's law, J = σE =  σ × $\frac{V}{L}$

                                   nev =   σ × $\frac{V}{L}$

                                    v = $\frac{\sigma v}{neL}$

     ∴ Drift velocity =  $\frac{\sigma v}{neL}$