**electric current**, the

**drift velocity of electrons**,

**current density**and the

**relation between electric current and drift velocity**, and the

**relation between current density and drift velocity**.

# Electric Current

The rate
of change flow of electric charge is called **electric current**. The electric current is denoted by symbol ‘*I *(**constant
current**)’ and ‘*i* (**time-varying current**)’. Mathematically,
the electric current is given by the electric charge divided by time, i.e.

`\I=Q/t`

Where, *Q* is the electric charge in **coulomb** and *t *is the time in **seconds**.
Therefore, the current is measured in **coulomb
per second (C/s)**, where,

1 C/s = 1 Ampere

# Drift Velocity

The **drift velocity** of free electrons is
defined as the average velocity with which the free electrons get drifted, i.e.
moved in a metallic conductor in a specific direction under the influence of an
electric field. It is denoted by *v _{d}*
and is measured in

**meters per second**.

Generally,
the drift velocity of the free electrons is of the order of 10^{-5}
m/s. However, the drift velocity of electrons is very small, but it is entirely
responsible for the flow of electric current in the metallic conductors.

# Relation between Current and Drift Velocity

Consider a
small portion of a **metallic conductor**
(say copper wire) through which a current of I amperes is flowing as shown in
the following figure.

*l* = length of the wire

*A* = area of cross-section of wire

Therefore, the volume (*V*) of the conductor wire is

`\V=A×l`

If *n* is the electron density, i.e. number
of free electrons per unit volume of the conductor, then,

Total number of electrons in the conductor
= *n × A × l*

Therefore,

Total
charge in the conductor, *Q* = *n × A × l × e*

Where, *e* is the charge on one electron and is
equal to –1.6×10^{-19} C.

If the
electron takes *t* seconds to cross the
conductor, then we have,

`\t=l/v_d`

Where, ** v_{d} **is the

**drift velocity of free electrons**.

Now, by
the definition of electric current, we have,

`\I=Q/t`

`\I={n eAl}/((l⁄v_d ) )`

Therefore,
the **relation between current and drift velocity **will be,

`\∴I=n eAv_d`

Since, for
a given conductor *n, e, A* are
constant. Therefore,

`\I∝v_d`

i.e. the electric current flowing through a conductor is directly proportional to the drift velocity of free electrons.

## Current Density

The
**current density **is defined as the current per unit area. It is denoted by the symbol *J* and is measured in **Ampere per square meter (A/m ^{2})**.

`\J=I/A`

Hence, the
**relation between current density and
drift velocity** can be established as follows,

`\J=(n eAv_d)/A`

`\∴J=n ev_d`

**Numerical Example** – The density of conduction
electrons in a copper wire is `\8.5×10^28" m"^(-3)`. If the radius of the wire is 0.8 mm and it is
carrying a current of 3 A, what will be the average drift velocity of
electrons?

**Solution** – Given data,

`\n=8.5×10^28" m"^(-3)`

`\I=3" A"`

`\r=0.8" mm"`

Therefore,
the area of cross-section (*A*) of the
wire is

`\A=Ï€r^2`

`\⟹A=Ï€×(0.8×10^(-3) )^2`

`\⟹A=2×10^(-6)" m"^2`

Now, since
we know that the relation between current and drift velocity is given by,

`\I=n eAv_d`

Therefore,
the drift velocity of electrons is given by,

`\v_d=I/{n eA}`

`\⟹v_d=3/((8.5×10^28 )×(1.6×10^(-19) )×(2×10^(-6) ) )`

`\∴v_d=1.1×10^(-4)" ms"^(-1)`

Hence, in
this article, we discussed about the **electric
current**, **drift velocity**, and the
**relationship between current and drift
velocity**.

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