课程名称︰普通物理学甲下 课程性质︰必修 课程教师︰蔡尔成 开课学院：理学院 开课系所︰大气系 考试日期（年月日）︰2011/06/21 考试时限（分钟）：120分钟 是否需发放奖励金：yes （如未明确表示，则不予发放） 试题 : → 1.[10%] A uniform magnetic field B is perpendicular to the plane of a circular wire loop of radius r. The magnitude of the field varies with time according to B = Bo*e^(-t/τ), where Bo and τ are constants. Find an expression for the emf in the loop as a function of time. 2.[10%] In an oscillation series RLC circuit, show that ΔU/U, the fraction of the energy lost per cycle of oscillation, is given to a close approximation by 2πR/ωL. 3.The magnetic field of Earth can be approximated as the magnetic field of a dipole. The horizontal and vertical components of this field at any distance r from Earth's center are given by μoμ μoμ B = ──── cosλ , B = ──── sinλ , h 4πr^3 m v 2πr^3 m where λ is the magnetic latitude (this type of latitude is measure from m the geomagnetic equation toward the north or south geomagnetic pole). Assume that Earth's magnetic dipole moment has magnitude μ = 8.00*10^22 A*m^2. (a)[5%] Show that the magnitude of Earth's field at latitude λ is given by ___________ m μoμ / 2 B = ──── / 1+3sin λ . 4πr^3 V m (b)[5%] Show that the inclination φi of the magnetic field is related to the magnetic latitude λ by tanφi = 2tanλ . m m 4.[10%] In Fig. 33-42, unpolarized light is sent into a system of three polarizing sheets. The angles θ1, θ2, and θ3 of the polarizing directions are measured counterclockwise from the positive direction of the y axis (they are not drawn to scale). Angles θ1 and θ3 are fixed, but angle θ2 can be varied. Figure 33-43 gives the intensity of the light emerging from sheet 3 as a function of θ2. (The scale of the intensity axis is not indicated.) What percentage of the light's initial intensity is transmitted o by the system when θ2 = 30 ? (课本有图) 5.[10%](37-21) If m is a particle's mass, p is its momentum magnitude, and K is its kinetic energy, show that (pc)^2 - K^2 m = ──────── . (考卷上此题并无附图) 2Kc^2 6.[10%] Two different surfaces S1 and S2 have the same boundary. Prove that the sum of current i and displacement current i passing through these two d surfaces are the same. i + i = i + i . 1 d1 2 d2 7.[10%] We may describe a device in an alternating-current circuit by complex __ current I = Io*e^(jωt) and complex voltage V = Vo*e^(jωt), where j = v-1. The physical current i for the device is the real part of the corresponding complex current, i = Re(I). Similar, the physical voltage v for the device is the real part of the corresponding complex voltage, v = Re(V). The V complex impedance Z = ── is defined as the ratio of complex potential over I complex current for a device in an alternating circuit. Prove the complex 1 impedance for capacitor C is ─── and the complex impedance for inductor jωC L is jωL. 8.[10%] What are the four Maxwell equations in both integral and differential forms? 9.[10%] For a plane traveling electromagnetic wave along the x axis with the eletric field → → ^ E (x , t) = Eo*cos(ωt-kx)j where ω 1 ── = ───── , ──── k V μoεo → → what is the magnetic field B (x , t)? 10.[10%] If two events (t1, x1), (t2, x2) occur at the same space point x1 = x2 but at different times t1 ≠ t2, show that it is impossible to find another inertial frame in which these two events occur simultaneously under special relativity. --

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