※ [本文轉錄自 NTU-Exam 看板] 作者: rexx () 看板: NTU-Exam 標題: [試題] 94下 張顏暉 普通物理學甲 期中考 時間: Sat Apr 22 00:22:52 2006 課程名稱︰普物甲下 課程性質︰ 課程教師︰張顏暉 開課系所︰電機系 考試時間︰2006/04/20 試題 : 1. A spherically symmetrical but non-uniform distribution of charge produces an eletric field of magnitude E=Kr^5, directed radially outward from the center of the sphere. Here r is the radial distancefrom that center. What is the volume density ρ(r) of the charge density? (10) 2. A large flat non-conducting surface has a uniform charge density σ. A small circular hole of radius R has been cut in the middle of the surface as shown in Fig.-1. What is the eletric field at point P, a distance z from the center of the hole along its axis? (10) ‧ p ｜＿＿＿ ／｜ ／ ／ ○ ／ ／ ／ ￣￣￣￣ 3. A capacitor is made of two concenteric spheres of radii a1 and a2 respectively, see Fig.-2. The space between the two spheres is filled with dielectric constant k=k0/r. What is the capacitance of this capacitor? (10) 4. Describe the operation of a cyclotron as shown in Fig.-3. Express the kinetic energy of a particle with mass m, charge q existing from a cyclotron with radius R and magnetic field B. (10) 5. Fig.-4 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. Find the magnetic field B at any point inside the hole. (10) 6. What is the magnetic moment of an electron orbiting around a uniform circle of radius a with speed v. Find the ratio between the angular momentum and magnetic moment of this orbiting electron. The electron is orbiting in the x-y plane, and the z-axis passes through the center of the orbit. Find the magnetic field produced by this electron at point p at the z-axis, and is at a distance z above the center of the x-y plane. (10) 7. Show that the energy density in a solenoid is B^2/2μ0 and the energy density in a parallel capacitor is ε0E^2/2 (10) 8. In Fig.-6, a rectangular loop of wire with length a, width b and resistance R isplaced near a infinitely long wire carrying current i. The loop then is moved away from the wire with constant speed v. When the center of the loop is at a distance r=2b, what are (a) The magnitude of the magnetic flux through the loop? and (b) the current induced in the loop? (15) a ┌────┐ v↑┬│ │b r│└────┘ ┴─────── i 9. Find the total current of the parallel RCL circuit, as shown in Fig.-7. (15) ε=εsinωt ┌─┬─┬─┐ │ │ │ │ ε⊙ R︴ Lξ C╪ │ │ │ │ └─┴─┴─┘ --

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