課程名稱︰普通物理學甲下 課程性質︰系必修 課程教師︰張寶棣 開課學院：電資學院 開課系所︰資訊系 考試日期（年月日）︰2008/05/09 考試時限（分鐘）：130 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. A wire is formed into a circle having a diameter of 10.0 cm and placed in an uniform magnetic field of 3.00 mT. The wire carries a current of 5.00 A. Find (a) the maximum torque on the wire and (b) the range of potential emergies of the wire-field system for different orientations of the circle. (10%) 2. Figure 1 shows a cross section of a long cylindrical conductor of radius a containing a long cylindrical hole of radius b. The axes of the cylinder and hole are parallel and are a distance d apart; a current i is uniformly distributed over the tinted area. (a) Use superposition to find the megnetic field at the center of the hole. (b) Discuss the two special cases b = 0 and d = 0. (c) Use Amphere's law to show that the magnetic field in the hole is uniform. (15%) 3. In Fig.2, both currents in the infinitely long wires are in the negative x direction. (a) Sketch the magnetic field pattern in the yz plane. (b) At what distance d along the z axis is the magnetic field a maximum (10%) 4. Fig.3 shows a rod of length L caused to move at constant speed v along horizontal conducting rails. The magnetic field i which the rod moves is not uniform but is provided by a current i in a long wire parallel to this rails. Assume that v = 5.00 m/s, a = 10.0 mm, L = 10.0 cm, and i = 100 A. (a) Calculate the emf induced in the rod. (b) What is the current in the conducting loop? Assume that the resistance of the rod is 0.400 Ω and that the resistance of the rails and strip the connect them at the right is negligible. (c) At what rate is the thermal energy being generated in the rod? (d) What force must be applied to the rod by an external agent to maintain its motion? (e) At what rate does this external agent do work on the rod? (20%) 5. Two inductors L1 and L2 are connected in parallel and separated by a large dustance. (a) Show that the equivalent inductance is given by 1 / Leq = ( 1 / L1 ) + ( 1 / L2 ). (b) Why must their separation be large for this relationship to hold? (10%) 6. A capacitor, a coil, and two resistors of equal resistance are arranged in an AC circuit, as shown in Fig. 4. An AC source provides an emf of 20.0 V (rms) at a frequency of 60 Hz. When the double-throw switch S is open, as shown in the figure, the rms current is 183 mA. When the switch is closed in position 1, the rms current is 298 mA. When the switch is closed in position 2, the rms current is 137 mA. Determine the value of R, C and L. Is more than one set of values possible? Explain your reasons. (15%) 7. A helium-neon laser of the type often found in physics laboratories has a beam power of 5.00 mW at a wavelength of 633 nm. The beam is focused by a lens to a circular spot whose effective diameter may be taken to be equal to 2.00 wavelengths. Calculate (a) the intensity of the focused beam, (b) the radiation pressure exerted on a tiny perfectly absorbling sphere whose diameter is that of the focal spot, (c) the force exerted on this sphere, and (d) the magnitude of the acceleration imparted to it. Assume a sphere density of 5.00 × 10 ^ 3 kg/m^3. (12%) 8. In Fig. 5, initially unpolarized light is sent through three polarizing sheets whose polarizing directions make angles θ1 = 40 degrees, θ2 = 20 degrees, and θ3 = 40 degrees with the direction of the y axis. What percentage of the light's initial intensity is transmitted by the system? (8%) --

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