課程名稱︰Electromagnetics I
課程性質︰必修
課程教師︰張宏鈞
開課系所︰電機系
考試時間︰2006.4.17 10:20~12:00
試題:
1.Let P and P' be the point with spherical coordinates (1,θ,ψ), (1,θ',ψ'),
respectively.Let O be the origin of the coorinate system. Find
→ →
1) the angle γ between the two vectors OP and OP',
2) the distance between the points P and P'
2.In Cartesian coordinate system, let S be the triangular plane defined by
→ → ^ ^ ^
x+y+z=1,0<x,y,z<1 and A be the vector given by A = 3 x + 2 y + z. Find
1) the unit normal vector to the plane S,
→ →
2) the surface integral ∫A‧dS over the plane S.
s
3.Two equal and opposite point charges +Q and -Q are located at (0,0,d/2)
and (0,0,-d/2), respectively. Such an arrangement is known as the electric
_ _ _
dipole. Find the electric field intensity E(r) at the point r, due to the
electric dipole, such that the spacing d is much smaller than the distance
_
r = |r| from the origin.
4.The Faraday disk generator consists of a circular metal disk rotating with a
constant angular velocity ω in a uniform and constant magnetic field of
_ ^
flux density B = z Bo that is parallel to the axis of rotation. Brush
contacts are provided at the axis and on the rim of the disk, as shown in
Fig.1. Determine the open-circuit voltage or emf of the generator if the
disk radius is b.
5.Let us consider the charge distribution given by
{ ρo x/a , -a < x < a
ρ = {
{ 0 , otherwise
_
where ρo (C/m^3) is a constant. Find the displacement flux density vector D
everywhere and plot D versus x.
6.A coaxial cable consists of an inner conductor of radius a and an outer
conductor (zero thickness) of radius b (b > a). Assume that the cable is
infinitely long and its axis is along the z-axis. Current I flows with
uniform density in the z-direction in the inner conductor and returns with
uniform density in the -z-direction in the outer conductor. Find the
_
magnetic field intensity H everywhere and plot H versus r.
7.Let an electric field in free space (μ_0,ε_0) be specified by
_ ^
E(z,t) = x e^j(ωt-βz) , j = √-1.
Find the condition on ω and β such that the field would satisfy both
Faraday's and Ampere's circuital laws.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 220.137.238.85