Suez Canal University (SCU)
Department of Electronics and Electrical Engineering
Sheet 1: Microwave Engineering (Part 2)
Dr.-Ing. Doaa Ahmed
Answer the following questions
1. An inductor is formed by winding N turns of a thin conducting wire into a circular loop of
radius a. The inductor loop lies in the x-y plane with its center at the origin and is connected
~ = B0 (ŷ2 + ẑ3) sin(ωt) is applied. Given the following
to a resistor R. A magnetic field B
parameters: N = 10, B0 = 0.2 T, a = 10 cm = 0.1 m, ω = 103 rad/s, and R = 1 kΩ
Find:
(a) The magnetic flux linking a single turn of the inductor.
(b) The transformer emf.
(c) The polarity of the transformer emf at t = 0.
(d) The induced current in the circuit.
z
B
I
R
B
1
+ V tr
− emf
2
y
a
N turns
2. Assignment: A 10-turn square loop, centered at the origin, with 20 cm sides oriented parallel
to the x- and y-axes, is placed in a time-varying magnetic field:
~ = ẑB0 x2 cos(103 t)
B
where B0 = 100 T. Find the current in the circuit.
3. Determine the voltages V1 and V2 across the 2 Ω and 4 Ω resistors in the circuit shown below.
The loop is in the x-y plane with an area of 4 m2 . The magnetic flux density is given as:
~ = −ẑ0.3t T
B
Additionally, the internal resistance of the wire is negligible.
4. A wire with conductivity σ = 2 × 107 S/m and relative permittivity εr = 1 carries a conduction
current Ic = 2 sin(ωt) mA, where ω = 109 rad/s. Find the displacement current.
I
y
x
4Ω
V1
V2
2Ω
Area = 4 m2
~
B
5. A poor conductor is characterized by a conductivity σ = 100 S/m and permittivity ε = 4ε0 ,
where ε0 = 8.85 × 10−12 F/m. At what angular frequency ω is the amplitude of the conduction
current density Jc equal to the amplitude of the displacement current density Jd ?
~ due to an infinitely long line
6. Use Gauss’s law to obtain an expression for the electric field E
with a uniform charge density ρL that resides along the z-axis in free space.
z
Uniform line
charge ρL
r
~
dS
h
~
D
Gaussian Surface
7. A slab of dielectric material has a relative dielectric constant of 3.8 and contains a uniform
electric flux density of 8 nC/m2 . If the material is lossless, find the following:
(a) The electric field intensity E.
(b) The polarization P .
(c) The average number of dipoles per cubic meter if the average dipole moment is 10−29 C·m.
8. A slab of Teflon extends from x = 0 to x = a in a uniform external electric field given by
Eout = E0 â V/m. In free space on both sides of the Teflon slab, the electric displacement field
is Dout = 0 E0 â and the polarization is Pout = 0. Determine the following fields inside the
Teflon slab:
(a) The electric displacement field Din .
(b) The electric field Ein .
(c) The polarization Pin .
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