In a conductor, applied voltage and current are proportional. This is not a "law," it's just a property of conductors, and serves as a definition of the concept of resistance. V = R I, and R = ρℓ/A, with R the resistance and ρ as the resistivity, to factor out the dependence on the physical dimensions of the conductor. It is also convenient to use a vector quantity to represent current. This quantity is called the current density, j. It is defined to point in the same direction as E. In terms of current, the magnitude of the current density can be defined as j = I/A, where A is the area of the conductor. Ohm's Rule can then be written as j = E/ρ. 
