1. (a) (i) Write down Maxwell's equations for static electric and magnetic ?elds in the vacuum (note that you should include charge and current densities).
(ii) How did Maxwell modify Ampére's law to account for dynamic electric ?elds?
(b) In a region of space in which the relative permittivity is (attached equation), the relative permeability is (attached), and the free current density is J = 0, the magnetic ?eld, B, is given by,
(attached equation)
Here A, k, and w are constants, t is time, x, y, and z are cartesian coordinates and i and j are unit vectors in the x and y directions respectively.
(i) Find the auxilliary ?eld, H.
(ii) Find the magnetisation, M.
(iii) Find delta * B and explain the physical meaning of your result.
(iv) Identify the circumstances in which delta * H = - delta * M.
(v) Find delta X B.
(vi) Find delta x E.
(vii) Does E = - delta V in this case?
(viii) Find delta E / delta t.
(ix) Deduce a possible expression for the electric ?eld, E.
(x) Find an expression for the polarisation vector, P.
(xi) Find the volume density of bound charge.
(xii) Find the volume density of free charge.
Attachment:- Phy 2.zip