What is Ohm's law in vector form.........???

@sunil.sahay92 has answered this question very well. Keep it up. This has been a great help to the users of this community. However I will briefly explain the Ohm’s law in vector form below.

Simply ohm’s law is:

V = IR where V is the potential difference, I is the current and R is the resistance.

Also R = pl/A where p is the resistivity which is material dependent parameter.

Now current density J is a vector quantity given by J_{z} = I/A if the conductor is aligned along z axis.

Substituting R in V = IR,

V = I * pl/A

Putting value of I/A = J

V = plJ

Also V/l is E which is a vector quantity , so

E = pJ

Or J = σE

Here σ is called conductivity and is 1/p , it is also material dependent.

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