課程名稱︰普通物理學 課程性質︰必帶 課程教師︰蔡爾成 開課學院：工學院 開課系所︰機械工程學系 考試日期（年月日）︰2011/04/22 考試時限（分鐘）：120分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(10%)(23-55)A charge of distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E=Kr^4, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and K is a constant. What is the volume density p of the charge distribution? 2.(10%)(23-65)What is the excess charge on a conducting sphere of radius r if the potential V=Vo at the sphere and the potential V=0 at infinity? 3.(10%)(25-50)Figure 25-49 show a parallel-plate capacitor of plate area A and plate separation 2d. The left half of the gap is filled with material of dielectric constant K1; the top of the right half is filled with material of dielectric constant K2; the bottom of the right half is filled with material of dielectric constant K3. What is the capacitance? 4.(10%)(26-37)Show that, according to the free-electron model of electrical conduction in metals and classical physics, the resistivity of metals should be proportional to T^1/2 ,where T is the temperature in kelvins. (此題附圖 請看課本對照) 5.(10%)(29-04)A straight conductor carrying current i=5.0A splits into identical semicircular arcs as shown in Fig.29-35. What is the magnetic field at the center C of the resulting circular loop? (此題附圖 請看課本對照) 6.(10%)Show that the electric field E(→) is perpendicular to the surface of a conductor is E(→)=0 inside the conductor. 7.(10%)A nonconducting solid sphere of radius a has a uniform charge density p. A spherical cavity of radius b is hollowed out of the sphere, as shown in the figure below. The center of the solid sphere and the spherical cavity are distance d apart. Show that the electric field in the hole is uniform. (此題附圖 一個半徑為a的球 中間挖一個半徑為b的球 a b球圓心距d) 8.(10%)A single isolated spherical conductor of radius a may be considered as a capacitor with the other conductor being a sphere at infinity (a)(5%)What is the capacitance? (b)(5%)Suppose charge Q is uniformly distributed on the sphere. What is the electrostatic energy? 9.(10%)Let B(→) be the magnetic field produced by a current loop of finite size carrying a steady current I, show that according the law of Biot and Savart ,at a distance r far away from the current loop, r^2B→0 as r→oo 10.(10%)In a certain cyclotron, a particle of charge q and mass m moves in a circle of radius R. The magnitude of the magnetic field is B. What is the kinetic energy of the particle? --

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