Vector form of ohm’s law

if E is the magnitude of electric field in a conductor of length I, then the Potential difference across its ends is

V = EI

Also, from ohm’s law, we can write,

E= Jρ

As the direction of current density j is same as that of electric field E, we can write the above eqⁿ as

     or   

The above equation is the vector form of ohm’s law. It is equivalent to scalar from, V = RI.