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課程名稱︰普通物理學甲下
課程性質︰系定必修
課程教師︰張顏暉
開課學院：電機資訊學院
開課系所︰電機工程學系
考試日期（年月日）︰6/26
考試時限（分鐘）：2.5hr
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1. For a RCL circuit connect with R//L//C and an ac power supply, assume that
the total current in the circuit is i=Im*sin(ωt). Find the currents in R,C,
and L, respectively.(15%) 註：有附圖，圖為R,L,C皆以並聯聯至交流電源。
2. Write down Maxwell's four equations for electromagnetism.(5%)
3. The electric field of an EM wave is given by E=Em*sin(ky-ωt)*k. What is the
travelling driection of this EM wave. Write down the expression for the
magnetic field of this EM wave(direction, magnitude and time dependence).
Find the expression for the intensity of this EM wave.(10%)
4. A perfectly flat piece of glass(n=1.5) is placed over a perfectly flat piece
of a black plastic(n=1.2) as shown in Fig. 1a.(圖請見Physis 5th. Hallidy
Resnick Krane vol.2 Figure 41-30). The location of the dark fringe in the
relected light is shown on the sketch Fig.1(b). (a)How thick is the space
between the glass and the plastic at B. (b)Water(n=1.33) seeps into the
region between the glass and the plastic. How many dark fringe are seen
when all the air has been dis placed by water.(10%)
5. A stack of polarizing sheet is arranged so that the angle between any two
adjacent sheets is α. The sheet are arranged so that N sheets rotate the
plane of polarization by θ where, θ=Nα. Caculate the fraction of the
light that will pass through the stack in the limit N->∞. Assume that θ
is fixed, so α->0.(10%)
6. Find the intensity I(θ) for the three slits diffraction-interference.
Assume the slit width is a and the separation between two adjacent slits is
d.(15%)
7. Write down the one-dimensional time independent Shrodinger equation for a
particle of mass m in a potential U(x).(5%)
8. Find the wave functions and energy levels of a particle with mass m and is
confirmed in a one dimensional infinite potential well with well width L.
9. For an electron in the ground state of the hydrogen atom calculate the
radius of a sphere for which the probability that the electron will be found
inside the sphere equals the probability that the electron will be found
outsite the sphere. Φ1s=(πa^3)^(-0.5)*e^(-r/a) (10%)
10.Describe how to slow donw an atom by photon bombardment(laser cooling)(10%)
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