Answer to Question #130141 in Electricity and Magnetism for K Ganesh

Question

Write don the four maxwell's equations in a region of space with charge density d and current density J and discuss qualitatively what each equation describing

Answer 1

J = Time varying current

H = Time varying magnetic field

E = electric filed

D = Electric flux densities (volt/m)

B =Magnetic flux densities (ampere/m)

Maxwell’s equations for all electromagnetic phenomena:

Maxwell's equation between E and B (Faraday’s law of induction)

$\triangledown\times E = - \frac{\partial B}{\partial t}$ ...1)

Maxwell's equation between H ,J and D(Amp`ere’s law )

$\triangledown\times H = J + \frac{\partial D}{\partial t}$ ...2)

Maxwell's equation between D and $\rho$

$\triangledown. D = \rho$ ...3) (Gauss’ laws)

$\triangledown. B = 0$ ... 4) (Gauss’ laws)

The first is Faraday’s law of induction, the second is Amp`ere’s law as amended by Maxwell to include the displacement current ∂D/∂t, the third and fourth are Gauss’ laws for the electric and magnetic fields.