Derivation of ohm's law.
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2
We know, according to Ohm's Law, V=iR, But R=
A
ρl
Hence V=
A
Iρl
Current per unit area (taken normal to the current), I/A, is calledcurrent density and is denoted by j.
Further, if E is the magnitude of the uniform electric field in the conductor whose length is l, then the potential difference V across its ends is El.
El=jl
the above equation can also be casted in vector form. The current density ( current through unit area normal to the current) is also directed along
E
and is also a vector J
Hence the above equation can be casted in vector form as
E
=σ
j
where σ=
ρ
1
is called the conductivity.
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