Derive the relation `vec(j)=sigmavec(E)` with terms which has usual meaning.

Explanation

We know from the Ohm.s law, I = KV
where, I- electric current,
K - conductance and V - potential difference
Dividing I= KVby `.^^.` on both sides we get,
`I/A=K/A V`
by definition electric current density `j=I/A`
Hence `j=(K/A)V`
But electric field ,
`E=V/l` or V=El
hence `j=(K/A)(El)`
where `sigma=(Kl)/A` is known as the electrical conductivity .
Hence `j=sigmaE`. In a vector form , the relation is written as `vecj=sigmavecE` .