Give the Relation between current density and conductivity?

Question

Arun · Answer

According to Ohm's law, the potential difference between ends of a conductor is directly proportional to the current, that is

V α I

Or V=IR (2)

Where R is resistance (that is obstruction offered to flow of changes)

Also, when a current I flows in a uniform cross-section area normally to it, then

I=∫J.ds

= ∫JdS cos 00

=J∫dS

I=JA (3) (where ∫dS = A)

Also, resistance R= ρl/A (4)

Equation (3) can also be written as

R=l/σA (5)

Where σ=1/ ρ is conductivity

Substituting equations (3) and (5) in equation (2) we get

V=JA*l/σA

V=Jl/σ

Or J=σV/l (6)

But electric field intensity E=V/l

By putting above value of E in equation (6),we get

J= σ E

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