Department of Electronic and Telecommunication Engineering, University of Moratuwa
EN4620 Antennas and Propagation—Quiz 01
Instructions: Answer all the questions. This is a closed-book quiz.
Q1. Write the Maxwell’s equations in integral form. Define the terms.
[6 marks]
I
Z
d
E · dl = −
B · dS.
dt S
C
Z
I
Z
d
D · dS.
H · dl =
J · dS +
dt S
C
S
Z
I
ρdv.
D · dS =
V
IS
B · dS = 0.
S
E: electric field intensity (volt/meter).
B: magnetic flux density (ampere/square meter).
H: magnetic field intensity (ampere/meter).
J : volume current density (ampere/square meter).
D: displacement flux density (coulomb/square meter).
ρ: volume charge density (coulomb/cubic meter).
Q2. Write the Maxwell’s equations in differential form, and the continuity equation. Define the
terms that you did not define above.
[6 marks]
∂B
.
∂t
∂D
∇×H =J +
.
∂t
∇ · D = ρ.
∇ · B = 0.
∇×E =−
Q3. Given in usual notation E = Em sin(ωt − βz)iy in free space, find D, B, and H. Sketch E
and H at t = 0 and t = π/(2ω).
[8 marks]
1
The Maxwell equation ∇ × E = −∂B/∂t gives
ix
i
i
y
z
∂
∂
∂
= − ∂B .
∂x
∂y
∂z
∂t
0 Em sin(ωt − βz) 0 or
−
∂B
= βEm cos(ωt − βz)ix .
∂t
Integrating
βEm
sin(ωt − βz)ix ,
ω
where the constant of integration, which is a static field, has been neglected. Then,
B=−
H=−
βEm
sin(ωt − βz)ix ,
ωµ0
E and H are mutually perpendicular. At t = 0, sin(ωt − βz) = − sin(βz). With this
information, we can sketch E and H at t = 0, and t = π/(2ω).
Sketches: Please see the simulation, EM Waves in Free Space.
2