the microscopic equivalent of the relation V=IR is J=E?

Question

is it true or false?

Answer 1

TRUE: Current density is the dot product of the conductivity and the electric field (in the absence of a magnetic field, otherwise you have to add to the electric field the cross product of the velocity and the magnetic field to get the combined Lorentz field).

I wouldn't call it microscopic--it's the fundamental electromagnetic relation, and it applies on all scales. It's just less useful for actual circuit work than the usual statement of Ohm's Law.

Answer 2

J - sigma * E where sigma is the conductivity.

Answer 3

not false