What is the direction of current density?

The equation that relates resistivity , Electric field and current density (j) is $E = J \times \rho$

Since resistivity is a scalar quantity the direction of J must be in the direction of Electric field. I'm confused as to which electric field it is - inside the conductor or outside the conductor. My tutor said it was the direction of external electric field but my textbook says ;

Current per unit area (taken normal to the current, is called current denisty . Further if E is the magnitude of uniform electric field in conductor whose length is l, then the potential difference V across it's ends is E x l.

This contradicts what my teacher said , moreover, I can't understand how there could be a non zero uniform electric field inside a conductor. I heard him say that when in a DC source the frequency is zero so there's no entering of charge into the conductor (skin depth).

• Resistivity is not always a scalar. For example graphite. – Pieter Mar 8 '18 at 14:54
• You are asking too many questions all at once which makes it difficult to follow. I will respond to two of your issues. When an electric field is applied to the conductor, charges will flow in response to the field. If the conductor is isolated, charges will accumulate on the surface so as to nullify the internal field. But if the charges continue along an external circuit, electric field inside the conductor will exist. Second issue, the book should say taken normal to the area rather than normal to the current. – npojo Mar 8 '18 at 14:56
• @npojo could you elaborate more and make it into a full fledged answer? my two concerns are (i) How is there an electric field inside the conductor when it's said that the field inside a conductor is zero? and (ii) If current density is no where in relation with the internal field how is it related to external field as external field's direction is opposite to current flow? – susan J Mar 8 '18 at 15:26
• How can an electron inside a conductor respond to a field outside (i.e., the external field). Those fields may be related, but the electrons respond to the local field. This may boil down to what, exactly, was the original question. – garyp Mar 8 '18 at 15:27
• So you mean to say that the net electric field inside the conductor must be non zero? But if the charges continue along an external circuit, electric field inside the conductor will exist How and why? – susan J Mar 8 '18 at 15:31