What is the Role of J in Dynamic Ohm's Law?

[berra]

Homework Statement

What is J in Ohms law in dynamics?

Homework Equations

Ampères law:
$$\nabla \times H = J_f + \partial_t D = J_f + \partial_t ( \epsilon_0 E + P)$$
$$\nabla \times H = \nabla \times (\mu_0^{-1} B - M) = \nabla \times (\mu_0^{-1} B) - \nabla \times (M) = \nabla \times (\mu_0^{-1} B) - J_m$$
$$\nabla \times (\mu_0^{-1} B) = J_m + J_f + \partial_t ( \epsilon_0 E + P)$$
Ohms law (statics?):
$$\sigma E = J$$
Relation between J and p (magnetostatics ?):
$$\int_V{ J dV} = \frac{dp}{dt} = \frac{d\int_{V'}{r' \rho{r'} dV'}}{dt}$$

The Attempt at a Solution

Is $J = J_m + J_f + \partial_t (P)$ ?

 

[member 553083]

I think J in Ohms law in dynamics is the same as the J in Ampères law in statics, which is equal to J_m + J_f + \partial_t (P).