Question

define the term current density of metallic conductor deduce the relation connecting current density J and conductivity Sigma of the conductor when electric field E is applied on it

Answer 1

Current density is the electric current per unit area of cross section.

Let I current flow through a conductor when applied potential difference V volt.
Now, from ohm’s law,
(deduce as shown in the picture attached)

Answer 2

Answer:

In a conductor, the current density at a certain point is the current flowing per unit area in the conductor delivered the area that exists in the direction expected to current.

Explanation:

Given,

• the relation connecting current density J and conductivity Sigma of the conductor when electric field E is applied to it

To find,

• define the term current density of metallic conductor

In a conductor, the current density at a certain point is the current flowing per unit area in the conductor delivered the area that exists in the direction expected to current.

$J\frac{I}{A}$

Current density is a vector quantity. Its direction is the direction of motion of the positive charge. The unit of current density is.

Step 1

$\frac{ampere}{meter} ^{2}$, or $[Am-2]$

Relation between$J$ and $E$:

$&\mathrm{I}=n \mathrm{Aev}_{d}=n \mathrm{~A} e\left(\frac{e \mathrm{E}}{m} \tau\right)$

$&\mathrm{I}=\frac{n \mathrm{Ae}^{2} \tau \mathrm{E}}{m}$

$&\frac{\mathrm{I}}{\mathrm{A}}=\frac{n e^{2} \tau \mathrm{E}}{m}$

$&\mathrm{~J}=\frac{1}{\rho} \mathrm{E}$

Step 2

$&{\left[\because \mathrm{J}=\frac{I}{A} \text { and } \rho=\frac{m}{n e^{2} \tau}\right]}$

$&\mathrm{J}=\sigma \mathrm{E} \quad\left[\because \sigma=\frac{1}{\rho}\right]$

#SPJ2