课程名称︰普通物理学甲下 课程性质︰系订必修 课程教师︰赵治宇 开课学院：工学院 开课系所︰化工系 考试日期（年月日）︰97.06.20 考试时限（分钟）：195分钟 是否需发放奖励金：是 试题 : 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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