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課程名稱︰普通物理學甲下
課程性質︰必修
課程教師︰趙治宇
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰2013/6/20
考試時限（分鐘）：170分
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Determine the inductance per unit length of a coaxial cable whose inner
conductor has a radius r1 and the outer conductor has a radius r2, shown
as Fig.1. The conductors are thin and carry equal current in opposite
direction. (10%) [筆記]
圖形就是兩個同心圓的管子，平行擺放，一個半徑r1，一個r2，然後電流在管壁上面跑
，裡面的管子電流朝左，外面的朝右，圖不好畫，所以用描述的。
圖應該在筆記『自感 』那邊。
2. 舉例說明並描述地磁反轉之證據。（10％） [筆記]
3. 推導光壓的大小為Pr = I/c (total absorption) 與 Pr = 2I/c (total reflection)
(10%) [HALLIDAY 899～900頁]
4. Describe the behavior of electric field of (a) a partially polarized light,
and (b) a circularly polarized light. (8％） [筆記]
5. Figure 2 shows a cross section of an infinite conducting sheet carrying a
current per unit x-length 入; the current emerges perpendicularly out of
the page. (a) Use the Biot-Savart law and symmetry to show that for all
points P above the sheet and all point P' below it, the magnetic field B
is parallel to the sheet and directed as shown. (b) Use Ampere's law to
prove that B = (1/2)miu0入 at all points P and P'. (12%) [789頁, 29-81]
6. Figure 3 shows a rod of length L = 10.0cm that is forced to move at a
constant speed v = 5.00 m/s along horizontal rails. The rod, rails, and
connecting strip at the right form a conducting loop. The rod has
resistance 0.400 omega; the rest of the loop has negligible resistance.
A current i = 100A through the long straight wire at distance a = 10.0mm
form the loop sets up a (nonuniform) magnetic field through the loop.
Find the (a) emf and current induced in the loop. (b) What is the magnitude
of the force that must be applied to the rod to make it move at constant
speed? (10%) [821頁, 30-33]
7. In an oscillating series RLC circuit, shows that deltaU/U, the fraction of
the energy lost per cycle of oscillation, is given to a close approximation
by 2piR/wL. The quantity wL/R is often called the Q of the circuit (for
quality). A high-Q circuit has low resistance and a low fraction energy
loss (=2pi/Q) per cycle. (10%) [856頁, 31-27]
8. Figure 4a is an one-axis graph along which two of the allowed energy value
(levels) of an atom plotted. When the atom is placed in a magnetic field of
0.8T, the graph changes to that of Fig.4b because of the energy associated
with miu(orb)*B.(We neglect miu(s) ) Level E1 is unchanged, but level E2
splits into a (closely spaced) triplet of levels. What are the allowed
values of ml associated with (a) energy level E1 and (b) energy level E2?
(c) In joules, what amount of energy is represented by the spacing between
the triplet level? (10%) [886頁, 32-32]
9. In Fig.5, an airtight chamber of length d = 5.0cm is placed in one of the
arms of a Michelson interferometer. (The glass window on each end of
chamber has negligible thickness.) Light of wavelength 入 = 500nm is used.
Evacuating the air from the chamber causes a shift of 60 bright fringes.
From these data and to six significant figures, find the index of
refraction of air at atmospheric pressure. (10%) [987頁, 35-81]
10. Derive this expression for the intensity pattern for a three-slit
"grating":
I = (1/9)Im (1 + 4cosfi +_4cos^2fi)
where fi = (2pi d sin(sita))/入 and a << 入 ( a is the width of slit, d is
the distance between two slits) (10%) [1019頁, 36-54]
11. Consider the resonant cavity produced by closing off the two ends of a
rectangular wave guide, at z = 0 and at z = d, making a perfectly
conducting empty box. Show that the resonant frequencies for both TE and
TM modes are given by
W(lmn) = c(pi)((l/d)^2+(m/a)^2+(n/b)^2)^(1/2),
for integers ;, m, and n. Find the associates electric and magnetic fields.
( c is the speed of light, a and b is the length and width of the
rectangular wave guide ) (10%) [不用會]
12. A surface of a glass plate is covered with a thin layer of water. Light
with the wavelength 入 = 0.68*10^(-6) m strikes the surface at the angle
30.0degree with respect to the normal to the surface, as shown in Fig.6.
Due to the evaporating of the water layer, the intensity of the reflected
light changes periodically. The time interval between the appearances of
the maximum of intensity is equal to 15.0 min. Indices of refraction of
glass and water are respectively 1.50 and 1.34. Find the rate of decrease
of the water layer thickness. (10%)
光源 \ | /
2 \ | /
\ | /
\| /
\ /
1 \30 |\ E / 3
\ | \ /
\ | \ /
_________\|___\/_B_____________________________
A | 1 |
|1 1 d
__________|_1__________|_______________________
D C
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