Question

What is current density ? Derive Ohm’s law in form of current density

Answer 1

Answer:

Equation (5) is the Microscopic Form of Ohm's Law in terms of conductivity, electric field intensity and current density.

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Answer 2

Answer:

Current Density:  The current density at a point in a conductor is the ratio of the current at that point in the conductor to the area of cross-section of the conductor at that point.

Mathematically, it can be expressed as follows

j = I/A

where I = current

A = area of cross-section

Ohm's Law:

As we know,

$V = \frac{m}{ne^2\tau} \frac{l}{A} I$

where V = potential difference

I = current

$\frac{m}{ne^2\tau} \frac{l}{A}$ = Resistance of the conductor

Now,

$\frac{V}{l} = \frac{m}{ne^2\tau} \frac{I}{A}$

But $\frac{V}{l} = E, \frac{m}{ne^2\tau} = \rho, \frac{I}{A}= j$

∴ E = ρj

where E = electric field

ρ = resistivity

j = current density

Also, ρ = 1/σ

E = (1/σ)j

j = σE

This is Ohm's Law in terms of current density.

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