課程名稱︰普通物理學
課程性質︰化工系定必修
課程教師︰趙治宇
開課學院：理學院
開課系所︰物理系開給化工系
考試日期（年月日）︰99/06/24
考試時限（分鐘）：10:20~13:10(170分鐘)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Describe briefly (a) the evidence of the universe expansion and (b)
the working principle cooling invested by Steven Chu. (4%,6%)
2. What's the working principle of tape recording and playback in
a video tape recorder. (4%,4%)
3. Design a experiment to show the existence of diamagnetic material. (8%)
4. What's the operating principle of polymer chain reaction (PCR)? (10%)
5. Describe (a) the behavior of electric field of partially polarized light,
and (b) what's the difference between unpolarized light and circularly
polarized light. (3%,6%)
6. Figure 1 shows a coil of N_2 turns wound as shown around part of a toroid
of N_1 turns. The toroid's inner radius is a, its outer radius is b, and
its height is h. Show that the mutual inductance M for the toroid-coil
combination is given by
μ_0 N_1 N_2 h b
M=-------------- ln--- (8%)
2π a
(不會畫圖(￣□￣|||)a)
7. A square loop of wire of edge length a carries current i. Show that the
magnitude of the magnetic field produced at a point on the central
perpendicular axis of the loop and a distance x from its center is.
4 μ_0 i a^2
B=-------------------------------- (8%)
π(4X^2 + a^2)(4X^2 + 2a^2)^1/2
8. In Fig. 2, after switch S is closed at time t = 0, the emf of the source is
automatically adjusted to maintain a constant i through S. (a) Find the
current through the inductor as a function of time. (b) At what time is the
current through the resistor equal to the current through the inductor?
(4%,4%)
S
┌﹨─┬┐
constant- ││
current R L
source- ││
└──┴┘
9. The fractional half-eidth Δω_d of a resonance curve, such as the ones in
Fig.3, is thw width of curve at half the maximum value of I. Show that
Δω_d /ω = R(3C/L)^ 1/2, where ω is the angular frequency at resonance.
Note that the ratio Δω_d / ω increases with R, as Fig. 3 shows. (8%)
(太複雜了......不好意思我不會畫)
10. Consider a solid containing N atoms unit volume, each atom having a
magnetic dipole moment (頭上有→)μ. Suppose the direction of (頭上有→)μ
can be only parallel or antiparallel to an externally applied magnetic
field (頭上有→)B (This will be the case if (頭上有→)μ is due to the spin
of a single electron). According to statistical mechanics, the probability
of an atom being in a state with energy U is proportional to e^(-U/kt),
where T is the temperature and k is Boltzmann's constant. Thus, because
energy U is -(頭上有→)μ * (頭上有→)B, the fraction of atoms whose dipole
moment is antiparallel to e^ (μB/kT) and the fraction of atoms whose
dipole moment is antiparallel to (頭上有→)B is proportional to e^(μB/kT).
Show that the magnitude of the magnetization of this solid is
M = Nμtanh(μB/kT). (8%)
11. In Fig 4, a microwave transmitter at height a above the water level of a
wide lake transmits microwaves of λtoward a receiver on the opposite shore,
a distance x above the water level. The microwaves reflecting from the
water interfere with the microwaves arriving directly from the transmitter.
Assuming that the lake width D is much greater than a and x, and that
λ >= a, find an expression that gives the values of x for which the signal
at the receiver is maximum. (8%)
( Hint: Does the reflection cause a phase change? )
▃─
▎↑a ─▂
▎↓ x│ ▏
========================
│------------------▏
D
12. Assume that the limits of the visible spectrum are arbitrary chosen as
430 and 680 nm. Calculate the number of rulings per millimeter of a
grating that will spread the first order spectrum through an angle of
20.0度. (7%)
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※ 編輯: spontrick 來自: 140.112.30.84 (06/24 20:15)