Show that `j = sigmaE` where symbols have their usual meanings.

Explanation

We know from the Ohm.s law, I= KV
where, I - electric current, K - conductance and V - potential difference
Dividing I= KV by .A. 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 = `sigma`E. In a vector form, the relation is written as `vecj=sigmavecE`