School of Electrical and Computer Engineering
ECEG-3103- Electrical Engineering Materials
Final Exam
Date: Jan 27, 2014
Allowed Time 2:30 hrs.
Required constants: 𝒎 𝒆 = 𝟗. 𝟏𝟏 𝒙 𝟏𝟎 −𝟑𝟏 𝒌𝒈 (𝑻𝒂𝒌𝒆𝒎∗𝒆 = 𝒎∗𝒉 = 𝒎 𝒆 )
𝒆 = 𝟏. 𝟔 𝒙 𝟏𝟎−𝟏𝟗 𝑪
𝒉 = 𝟔. 𝟔𝟐𝟔 𝒙 𝟏𝟎−𝟑𝟒 𝑱𝒔
𝑱
𝑲 = 𝟏. 𝟑𝟖𝒙𝟏𝟎−𝟐𝟑
𝑲
−𝟏𝟐
𝜺 = 𝟖. 𝟖𝟓 × 𝟏𝟎
𝑭/𝒎
𝑨𝒕𝒐𝒎𝒊𝒄 𝒓𝒂𝒅𝒊𝒖𝒔 = 𝟎. 𝟏𝟐𝟓𝒙𝟏𝟎−𝟗 𝒎
Part I: (15 pts)
1. Briefly Explain the BCS Theory of superconductivity.
2. Explain the different polarization mechanism of dielectric property of insulating materials.
3. Explain the existence of magnetic dipole moments in atomic level; and Drive the simplest atomic
level magnetic dipole moments (orbital magnetic dipole moments).
Part II:
4. (5 pts) The critical field for Niobium is 12.5 × 10−2 tesla at 8 °K and 25.7 × 10−2 tesla at
absolute zero. Find the critical transition temperature (𝑇𝐶 ) of the element to be changed to
superconducting material.
5. (12 pts) A dielectric material has 1028 atoms per unit volume. If the internal (local) electric
field𝐸𝑖𝑛𝑡 = 0.015 𝑉/𝑚 , calculate the external applied field, assuming orientational polarization
to be negligible and ionic polarizability = 0.1 electronic polarizability.
6. (10 pts) A certain dielectric, when subjected to an alternating field of frequency𝑓1 = 4𝐺𝐻𝑧, has
a measured real part of the complex permittivity of 2.57 and the tangent of loss angel is
measured to be 0.0032. Determine
a. The imaginary part of the relative permittivity
b. The power dissipated in the dielectric per unit volume if a field of
𝐸 = 100 𝐶𝑜𝑠 2𝜋𝑓1 𝑡 𝑉/𝑚 is applied.
7. (8 pts) Find the paramagnetic magnetization of a material under normal temperature conditions
of T 300 °K if the applied magnetic field intensity is 3 𝑥 10−6 A/m and the atoms of the
material have atomic radii 𝑎 = 0.125 𝑥 10−9m. [Take ω =
e2
4πε0 𝒎 𝒆 a 3
for the internal magnetic
dipole moment].
8. (Bonus:6 pts ) A type II (hard) type superconductor reaches its vertex state at 𝐵𝑐1 0 = 1.75 ×
10−2 tesla. calculate the value of opposing magnetization M inside the superconductor at value
𝐵 = 10−1 tesla . If 1/3 of the magnetic field is able to penetrate the superconductor at that
point.
Good luck!