Question

derive microscopic ohms law J=oE and connect it with V=IR​

Answer 1

From Ohm's law,

I=

R

V

⟹J=

A

I

=

RA

V

=

A

ρl

A

El

=

ρl

El

=

ρ

E

=σE

Hence in vector form,

Answer 2

From Ohm's law,

$\bf I= \frac{R}{V}$

$\sf \: ⟹ j = \frac{i}{a} = \frac{v}{ra}$

$= \sf \: \frac{El}{ \frac{p1}{a} a}$

$= \sf \: \frac{El}{p1}$

$= \sf \: \frac{E}{P} = σE$

Hence in vector form,

$\sf \: J=σE$