課程名稱︰普通物理甲下 課程性質︰必修 課程教師︰趙治宇 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰2010/04/30 考試時限（分鐘）：180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.Using the energy band diagram to describe the difference among conductor, semiconductor, and insulator. (8%) 2. Describe the working principle of scan tunneling microscope. (10%) 3. State briefly the phenomenon of Hall effect and its application. (8%) 4. Explain the mechanism of the low-temperature superconductivity. (8%) 5. Describe the operating principle of time- of-flight mass spectroscopy. (8%) 6. From the "molecular point of view", why the electric field in a capacitor should decrease when a dielectric is inserted? (8%) 7. In Fig. 1, a conductor carries 6.0 A along the closed path abedefgha running along 8 of the 12 edges of a cube of edge length 10 cm. (a) Taking the path to be a combination of three square current loops (befgb, abgha, and cdefc), find the net magnetic moment of the path in unit-vector notation. (b) What is the magnitude of the net magnetic field at the xyz coordinates of (0,5.0 m, 0)? (4%, 4%) 8. In Fig. 2, a rectangular loop carrying current lies in the plane of a uniform magnetic field of magnitude 0.040 T. The loop consists of a single turn of flexible conducting wire that is wrapped around a flexible mount such that the dimensions of the rectangle can be changed. (The total length of the wire is not changed.) As edge length x is varied from approximately zero to its maximum value of approximately 4.0 cm, the magnitude τ of the torque on the loop changes. The maximum value of τ is 4.80 x 10^-8 N . m. What is the current in the loop? (8%) ┌────────┐ │ │ │ │ │ │ └────────┘ ├─── x ───┤ Fig. 2 9. The circuit of Fig. 3 shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, what is the charge on the capacitor? Assume C = 10μF ε_1= 1.0 V, ε_2= 3.0 V, R_1 = 0.20 Ω ,and R_2 = 0.40 Ω. (8%) switch ┌─*／*─────┬────────┐ - │ ε_1 │ ε_2 │- ┴ ↓ │ ↓ ┴ + ￣￣ ─┴─ ￣￣+ │ ─┬─ C │ ＜ │ ＜ R _1 ＞ │ ＞ R_2 ＜ │ ＜ ＞ │ ＞ │ │ │ └────────┴────────┘ Fig. 3 10. Figure 4 shows wire section 1 of diameter D_1 = 4.00R and wire section 2 of diameter D_2 = 2.00R, connected by a tapered section. The wire is copper. and carries a current. Assume that the current is uniformly distributed across any cross-sectional area through the wire's width. The electric potential change V along the length L = 2.00 m shown in section 2 is 10.0μV. The number of charge carriers per unit volume is 8.49×l0^28 m^-3. What is the drift speed of the conduction electrons in section 1? (8%) ──╥──╮╞══L══╡ ║ ╰────╥─ D_1 D_2 ║ ╭────╨─ ──╨──╯ (1) (2) Fig.4 11. In Fig. 5, a nonconducting spherical shell of inner radius a = 2.00 cm and outer radius b = 2.40 cm has (within its thickness) a positive volume charge density ρ= A/r, here A is a constant and r is the distance from the center of the shell. In addition, a small ball of charge q = 45.0 fC is klocated at that center. What value should A have if the electric field in the shell (a<=r<= b) is to be uniform? (8%) 12. Fig. 6 shows an electric quadrupole. It consists of two dipoles with dipole moments that are equal in magnitude but opposite in direction. Show that the value of E on the axis of the quadrupole for a point P a distance z from its center (assume z>>d) is given by E = 3Q/(4π．ε_0． z^4) in which Q (=2qd^2) is known as the quadrupole moment of the charge distribution. (10%) ├──────z───────┤ ├─ d─┼─ d─┤ │ ●-----○○-----●───────── ⊙ +q -q-q +q p Fig.6 圖在課本都有(v. 8) --

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