Question

Show that `vec E = rho vec j` leads to Ohm’s law.

Answer 1

E = ρJ

Since, J = `I/A`

Thus, E = `(rho I)/A`

Multiply by L in the numerator and denominator,

E = `((rho I)/A) xx (L/L)` and

`(rho L)/A` = R

E = `R xx I/L`

Thus, E × L = R × I

Since, E × L = V

Thus, V = IR, which is Ohm’s law.

Hence proved.