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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Answer 1

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 $E = \frac{V}{L}$
When $V$ = potential difference across the conductor and $L$ =length of the conductor
The electric field exerts an electrostatics force ' $- E e$ ' on each free electron in the conductor
The acceleration of each electron is given by
$\overset{a}{ˉ} = - \frac{e E}{m}$
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.
$v_{d} = \frac{c E}{m} τ$ ...............(i)
$E = \frac{- V}{L}$ ...........(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 = $n A L$
Total charge on the conductor , $q = n A L e$
Time taken by this charge to cover the length $L$ of the conductor,
$t = \frac{L}{v _{d}}$
Current $I = \frac{q}{t}$
$= \frac{n A L e}{L} \times v_{d}$
$= n A e v_{d}$
Using equation (i) and (ii), we get that
$I = n A e \times (- \frac{e ( - V )}{m L} τ)$
$= (\frac{n e ^{2} A}{m L} τ) V$

Answer 2

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 = \frac{V}{L}

When

V

= potential difference across the conductor and

L

=length of the conductor
The electric field exerts an electrostatics force '

- E e

' on each free electron in the conductor
The acceleration of each electron is given by

\overset{a}{ˉ} = - \frac{e E}{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.

v_{d} = \frac{c E}{m} τ

...............(i)

E = \frac{- V}{L}

...........(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 =

n A L

Total charge on the conductor ,

q = n A L e

Time taken by this charge to cover the length

L

of the conductor,

t = \frac{L}{v _{d}}

Current

I = \frac{q}{t}

= \frac{n A L e}{L} \times v_{d}

= n A e v_{d}

Using equation (i) and (ii), we get that

I = n A e \times (- \frac{e ( - V )}{m L} τ)

= (\frac{n e ^{2} A}{m L} τ) V

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Revise with Concepts

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Mobility

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'.

A and B are two observes looking at a current carrying conductor, While A is stationery B is moving opposite to the direction of current in the conductor assuming that all the electrons in the conductor move the same drift velocity Vd. If B moves with Vd along xx', then

A current i is flowing through the wire of diameter d having drift velocity of electrons vd​ in it. What will be new drift velocity when diameter of wire is made 4d​?

Define the term 'drift velocity' of charge carriers in a conductor and write its relationship with the current flowing through it.

When current i is flowing through a conductor, the drift velocity is v. If the value of current through the conductor and its area of cross-section is doubled, then new drift velocity will be

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Revise with Concepts

Advanced Knowledge of Drift Velocity

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Mobility

A current $i$ is flowing through the wire of diameter $d$ having drift velocity of electrons $v_{d}$ in it. What will be new drift velocity when diameter of wire is made $\frac{d}{4}$ ?

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