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Give the Relation between current density and conductivity?
According to Ohm's law, the potential difference between ends of a conductor is directly proportional to the current, that isV α IOr 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, thenI=∫J.ds= ∫JdS cos 00=J∫dSI=JA (3) (where ∫dS = A)Also, resistance R= ρl/A (4)Equation (3) can also be written asR=l/σA (5)Where σ=1/ ρ is conductivitySubstituting equations (3) and (5) in equation (2) we getV=JA*l/σAV=Jl/σOr J=σV/l (6)But electric field intensity E=V/lBy putting above value of E in equation (6),we getJ= σ E
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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