- #1
roam
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Homework Statement
Consider a region of space containing static free charge density ρ(r) and current density j(r). What two physical laws determine the electric and magnetic field in this region?
State the integral form of each law, showing the explicit dependence of each on ρ(r) and j(r)
Homework Equations
Maxwell's equations in general differential form:
##\nabla . E =\frac{\rho}{\epsilon_0}##
##\nabla .B = 0##
##\nabla \times E = \frac{-\partial B}{\partial t}##
##\nabla \times B = \mu_0 J + \mu_0 \epsilon_0 \frac{\partial E}{\partial t}##
Maxwell's equations in matter in terms of free charges and currents:
##\nabla . D = \rho_f##
##\nabla .B=0##
##\nabla \times E = \frac{- \partial B}{\partial t}##
##\nabla \times H = J_f + \frac{\partial D}{\partial f}##
The Attempt at a Solution
I think the question is referring to Maxwell's equations, is that right? If so I'm not sure which set of equations I must to be looking at. By "static charge", does the question imply that there are no alternating currents? If that's the case the last term of the last equations must vanish.
The 2nd set is for inside of materials that are subject to electric and magnetic polarization and I'm not sure if that's the correct assumption here. But if we use this #1 and #4 make explicit dependence on ρ and j, are these the right equations?
So the integral forms are:
##\oint_S D. da = \int_V \rho_f dV = Q_{fenc}##
##\oint H . dl = \int_V j(r) dV = I_{fenc}##
I'm not sure if this is what the question is asking. So any helps is appreciated.