A plane wave in free space ( z<0) is incident normally on a large block of material with Er=12,Mr(meow),=3 which occupies z >0. If the incident electric field is E=30 cos(wt-z)ay V/m find: (a) wave speed,u and polarization direction (b) the standing wave ratio, (c) the transmitted and reflected magnetic field, Ht and Hr
- A plane wave in free space ( z<0) is incident normally on a large block of material with Er=12,Mr(meow),=3
which occupies z >0. If the incident electric field is E=30 cos(wt-z)ay
V/m
find:
(a) wave speed,u and polarization direction
(b) the standing wave ratio,
(c) the transmitted and reflected magnetic field, Ht and Hr
2.a) An EM field is said to be nonexistent or not Maxwellian if it fails to satisfy Maxwell’s equations and the wave equations derived from them. State whether the following field in free space is Maxwellian or not.
E=100sin(10^8t+x/root3)a^z .
- If it is Maxwellian; find the magnetic field, H.
2.b) Suppose E fields and H fields are:
E=Eoej(k.r-wt)
H=Hoej(k.r-wt)
k = kxax + kyay + kzaz and r = xax+yay+zaz
Show that Nabla *E=-db/dt can be expressed as K * E = mwH and deduce ak * aE = aH
For the same fields:
Show that Maxwell’s equation in a source-free region can be written as
k.E = 0
k.h=0
k * E = mwH
k * H = -mwH
From these equations deduce ak * aE = aH and ak * aH = -aE
3.a) The region between x = 0 and x = d is free space and has pv=po(x-d) If
V(x = 0) = 0 and V(x = d) = V0, find:
(i) V and E,
(ii) the surface charge densities
at x = 0 and x = d
b.Determine the magnetic flux through a rectangular loop (a × b) due to an infinitely long
conductor carrying current I as shown in the diagram.
The loop and the straight conductors are separated by distance d.
c.The y- and z-axes, respectively, carry filamentary currents 10 A along and 20 A
along. Find H at ( - 3 , 4, 5).
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