Answer to Question #178182 in Electricity and Magnetism for Vincent

Question

State Maxwell’s equations in terms of electric (E) and magnetic (B) fields in a region in which 

there are charge and current densities (p and J respectively) which are functions both of space and 

time. 

Answer 1

Answer

The fourth equation of Maxwell

$\Delta\times B=\mu _0J_{total }\\=\mu _0(J_f+J_d) \\=\mu _0(J_f+\frac{dD}{dt}) \\=\mu _0(J_f+ \epsilon_0\frac{dE}{dt})$

Where f indicates free and d for diffusion.