課程名稱︰普通物理學甲下
課程性質︰系訂必修
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）︰97.06.20
考試時限（分鐘）：195分鐘
是否需發放獎勵金：是
試題 :
1.In a double-slit experiment, the wavelength of the light source is 405 nm,
the slit separation is 19.44μm, and the slit width is 4.05μm. (a) How many
bright fringes are within the central peak of the diffraction envelope? (b) How
many bright fringes are within either of the first side peaks of the
diffraction envelope? (3%,4%)
2.(a) Show that the dispersion of a grating at angleθ is given by D=m/(dcosθ)
, whrer m is an integer and d is the separation between adjacent grating
rulings. (b) Show that the resolving power of a grating is given by R=Nm, where
N is the number of grating rulings. (3%,4%)
3.Describe the principle of Michelson's interferometer and its applications.
(6%)
4.(a) What is a partially polarized light? (b) What is a circularly polarized
light? (3%,4%)
5.Show that the traveling velocity of an electromagnetic wave is
c=1/(ε0μ0)^1/2. (6%)
6.Design an experiment how to prove the existence of diamagnetic materials.(6%)
7.In Fig.1 a broad beam of light of wavelength 630nm is incident at 90° on a
thin, wedge-shaped film with index of refraction 1.50. An observer intercepting
the light transmitted by the film sees 10 bright and 9 dark fringes along the
length of the film. By how much does the film thickness change over this length
? (7%)
8.Fig.2 shows a rod of length L=10.0cm that is forced to move at constant speed
v=5.00m/s along horizontal rails. The rod, rails, and connecting strip at the
right form a conducting loop. The rod has resistance 0.400Ω; the rest of the
loop has negligible resistance. A current i=100A through the long straight wire
at distance a=10.0mm from the loop sets up a (nonuniform) magnetic field
through the loop. Find (a) emf. (b) At what rate is thermal energy generated
in the rod? (c) What is the magnitude of the force that must be applied to the
rod to make it move at constant speed? (2%,2%,3%)
9.In Fig.3a, switch S has been closed on A long enough to establish a steady
current in the inductor of inductance L1=5.00mH and the resistor of resistance
R1=25.0Ω. Similarly, in Fig.3b, switch S has been closed on A long enough to
establish a steady current in the inductor of inductance L2=3.00mH and the
resistor of resistance R2=30.0Ω. The ratio Φ02/Φ01 of the magnetic flux
through a turn in inductor2 to that in inductor1 is 1.50. At time t=0, the two
switches are closed on B. At what time t is the flux through a turn in the two
inductors equal? (7%)
10.For the wire arrangement in Fig.4, a=12.0cm and b=16.0cm. The current in the
long straight wire is given by i=4.50t^2-10.0t, where i is in amperes and t is
in seconds. (a) Find the emf in the square loop at t=5.00s. (b) What is the
direction of the induced current in the loop? (6%)
11.An RLC circuit such as that of Fig.5 has R=5.00Ω, C=20.0μF, L=1.00H, and
εm=30.0V. (a) At what angular frequency ωd will the current amplitude have
its maximum value? (b) At what frequencies will the current amplitude be half
of its maximum value? (3%,4%)
12.In Fig.6, a capacitor with circular plates of radius R=18.0cm is connected
to a source of emfε=εmsinωt, where εm=220V and ω=130rad/s. The maximum
value of the displacement current is id=7.60μA. Neglect fringing of the
electric field at the edges of the plates. (a) What is the maximum value of
dΦE/dt, where ΦE is the electirc flux through the region between the plates?
(b) What is the separation d between the plates? (c) Find the maximum value of
the magnitude of B between the plates at a distance r=11.0cm from the center.
(2%,2%,3%)
13.The magnetic component of a polarized wave of light is
Bx=(4.0×10^-6T)sin[(1.57×10^7m^-1)y+ωt]
(a)Parallel to which axis is the light polarized? What are the (b) frequency
and (c) intensity of the light? (2%,2%,3%)
14.A thin flake of mica (n=1.58) is used to cover one slit of a double-slit
interference arrangement. The central point on the viewing screen is now
occupied by what had been the seventh bright side fringe (m=7). If λ=550nm,
what is the thickness of the mica? (7%)
15.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 (6%)
4μ0ia^2
B(x)= ──────────────
π(4x^2+a^2)(4x^2+2a^2)^1/2
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