| 1. |
A lossy dielectric slab of conductivity σ and permittivity ε is filled in the parallel-plate capacitor of area S and spacing d. For the time t = 0, shown as in Fig.1 the switch is closed in connection to the applied voltage V0.
| a) |
Plot the equivalent circuit (2%) and calculate the relaxation-time: τR = RC and sketch It curve using the circuit theory. (5%) |
| b) |
Under what condition (2%) that derives also the relaxation-time:  using the electrostatics (3%) and the equation of continuity (3%). |
|
| 2. |
As illustrated in Fig.2, a voltage V0 is applied across a parallel-plate capacitor. The space between the conducting plates is filled with two different lossy dielectrics of thicknesses d1 and d2 , permittivities ε1 and ε2 , and conductivities σ1 and σ1 , respectively.
| a) |
Find the relationship of material parameters that satisfies no induced surface charge density ρsi = 0 at the interface of the dieletrics. (10%) |
| b) |
If the above-mentioned slabs are perfect dielectrics of ε1 and ε2 (that is σ1 = σ2 = 0 & ε2 ＞ε1 ), determine the electrostatic force exerting on the upper dielectric slab. (10%)
|
|
| 3. |
An infinite conducting cone of half-angle α is maintained at potential V0 and insulated from a grounded conducting plane (V = 0 ), as sketched in Fig.3. Determine
| a) |
the electric field  (R,θ) in the range α＜θ＜π/2, (5%) |
| b) |
the capacitance C between the cone surface and the grounded plate assuming for unit height h = R. (10%) |
| |
| Hint： |
 |
| |
 |
|
|
| 4. |
A suggested scheme for reducing eddy-current power loss in transformer
cores with a circular cross section is to divide the cores into a large
number of small insulated filamentary parts. As shown in Fig.4 the section
illustrated in part (a) is replaced by that in part (b). Assuming that
 and that N
filamentary areas fill 95% of the original cross-sectional area, find
the total average eddy-current power loss in the N
filamentary sections P'av in relation to that of
Pav in the section of core of height h . (15%) |
| 5. |
A cylindrical permanent magnet of radius  and  length has a uniform magnetization along its axis that is shown in Fig.5. Solve the far field of  at the point  , for  and  using the similarity of electric dipole. (15%)
|
| 6. |
The far field of a short vertical current element  located at the origin of a spherical coordinate system in free space is
(V/m)
where  is the wavelength.
| a) |
Write the expression for instantaneous Poynting vector. (10%) |
| b) |
Find the total average power radiated by the current element. (10%) |
|
