# Ohm's Law for moving charge

1. Apr 5, 2012

Dear Fellows I have just came across with the basics of electromagnetism, and about the application of electric and magnetic force on charge particle,

Ohm's law for charge is
j=σE (1)
if the charge is moving with the speed "u"
then, j=σ(E+u$\times$ B) (2)

force on a charge by electric field is
F=q.E (3)
if the charge is moving through the electromagnetic field,
F=q(E+u$\times$B) (4)

I am supposed to use equation of motion for solid particles i.e.,
σ_ij,j+f_i=ρu'_i (u'=acceleration ' is for time derivative) (5)

my questions are
1- How equation (1) is converted to equation (2) if the partical started moving ??
2- similarly how equation (3) is converted to equation (4)
3- in final form eq (5) if found f_i = lorantz force but in (5) they use f_i =J$\times$B, why they did not use equation (4) in this situation.