Question

Obtain the relation between the drift velocity and current density.

Answer 1

Explanation:

Avarage velocity of free flowing electron of obtain electron applying potantial differens is known as drift velocity.

Answer 2

The relation between the drift velocity and current density is $\bold{\frac{I}{A} \infty \mathrm{V}_{\mathrm{d}}}$

Explanation:

Length of the conductor be l

Area of the conductor be A

Now, the volume of the conductor is:

$\bold{Volume =Al}$

Let number of free electrons be n

Let charge of free electrons be e

Now, the charge of the conductor is given as:

$\bold{Q=Volume\times Charge = Al\times ne}$

The electric field through the conductor is produced by the battery connected.

Now, the electric field is:

$\bold{E=\frac{V}{I}}$

After the battery is switched ON, the drift velocity and free electrons start to move.

So, the time take for the free electrons to cross the conductor is:

$\bold{t=\frac{l}{v_d}\longrightarrow (2)}$

Now, the current is charge per unit time.

$\bold{I=\frac{q}{t}\longrightarrow (3)}$

On substituting the equation (1) and equation (2) in equation (3), we get,

$\bold{\mathrm{I}=\frac{\mathrm{A} \ln \mathrm{e}}{\mathrm{l} / \mathrm{v}_{\mathrm{d}}}}$

$\bold{I = Anev_d}$

The current density is current per unit area.

$\bold{\therefore \frac{I}{A} \infty \mathrm{V}_{\mathrm{d}}}$