Ratch wrote:

Every solid had a property called resistivity. Resistance is determined by
the resistivity, the shape of the solid, and the
placement of the two measurement leads into the solid.

Prof Serway says the same thing about resistance/resistivity as L&M, except
Serway does not call the formula E=rho*J Ohm's law. Instead Serway says
that if the resistivity (rho) is constant at any electric field (E), then
the material is ohmic. That means that E and J are linearly proportionate to

The equation:

E = rho * j

says that for a constant rho, E is proportional to j. Serway is just
putting the equation to words.

each other. How does L&M define an ohmic material? Ratch

L&M say that, "Materials that obey Ohm's Law are usually called ohmic
conductors. This relation (Ohm's law) enables us to calculate the
current flowing through a wire of length L which is connected to
two terminals - points between which there is a potential difference V."

He then goes on to derive E = R * I from E = rho * j.

If you define R = rho * L/A, (R = rho * length/crossectional area)

and realize that V = |E| * L, (V = electric field strength * length)

you get:

V = rho * (L/A) * I = V = R * I, Ohm's law.

-Chuck