課程名稱︰電磁學
課程性質︰
課程教師︰江衍偉
開課學院：
開課系所︰電機系
考試日期（年月日）︰2007/4/23
考試時限（分鐘）：120mins
是否需發放獎勵金：是
（如未明確表示，則不予發放）
這篇沒有OP喔 雖然同是電磁學可是教授不同，考題也不同<(￣︶￣)>
試題 :
1.Find the algegraic equation for the direction lines for the vector field
given in spherical coordinates by (5cosθr+sinθθ)
(黃字代表單位向量)
2.(a)What is the Biot-Sarvart law? Statei its mathematical expression.
(b)Is it exactly valid for computing the magnetic field due to a
time-varying current distribution?
3.(a)What is Gauss' law for the electric field? Describe it both in integral
form and in differential form.
(b)Is it valid for the case of time-varying source and field distribution?
4.In a Cartesian coordinate system, constant current I flows along a straight
wire from a point charge Q1(t) located at the origin to a point charge Q2(t)
located at (0,0,5).
(a)Find the line integral of magnetic field H along the square closed path
having the vertices at (5,5,0),(-5,5,0),(-5,-5,0) and (5,-5,0) and
traversed in that order. (Express the answer in terms of current I)
(b)If the current I is time-varying, i.e.,I=I(t),(0<z<5),does the answer
in (a) need to be modified? Explain why.
(c)if Q2(t) is slowly moved from (0,0,5) to the origin (keeping I constant),
how does the answer of (a) gradually change? Explain briefly.
5.For the electric field E(y,z,t) = xexp(-αy)cos(ωt-βz) in free space
(μ0,ε0), find the necessary condition relating ω,α,β,μ0 and ε0
for the field to satisfy both of Maxwel's curl equations.
(x是x方向單位向量)
6.A rectangular loop of conducting wire with three sides foxed and the fourth
side movable is situated in a plane perpendicular to a uniform magnetic flux
density B=y0.5wb/m^2, as illustrated in Fig.P.6.(附圖於下)
A battery V_B=12V and a resistor R=4ohm are connected in series to the loop.
The movable side consists of a conducting rod of length l=1m and of mass 0.2kg
Assume that the resistance of the conducting wire and the movable rod is 0.
(a)With no friction and no load on the rod, calculate its initial acceration
and final velocity (in vector form)
(b)If the rod must pull a load requiring a force of 1 nt in the x-direction,
what will be its final velocity (in vector form)
(c)If the system is to act as a generator to produce a 1A charging current
through the battery, in what direction and how fast must the rod be pulled?
(d)How much force (in vector form) is required to maintain this motion?
(e)Calculate the electric power delivered by the rod and compute this with
the mechanical power delivered to the rod.
____________________________|_____...
電池V_B |
| ⊕磁場B |a rod(不是A-rod..冷)
| |
電阻R | z方向指向上方，x指向右方
∟__________________________|_____ ...
|
7.Consider a vector field A=-mysinxx+cosxy (黃色表單位向量)
(a) Evaluate the line integral ∫A dl from point (x1,y1,z1) to (x2,y2,z2)
along the straight line connecting them.
(b) Find ▽×A
(c) Use the results of (a) and (b) to verify Stoke's theorem.
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