# Current density and Ohm's law

1. Oct 18, 2011

### berra

1. The problem statement, all variables and given/known data
What is J in Ohms law in dynamics?
2. Relevant 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 ?):
$$\int_V{ J dV} = \frac{dp}{dt} = \frac{d\int_{V'}{r' \rho{r'} dV'}}{dt}$$
3. The attempt at a solution
Is $J = J_m + J_f + \partial_t (P)$ ?

Last edited: Oct 18, 2011