課程名稱︰普通物理學甲下 課程性質︰必帶 課程教師︰林敏聰 開課學院：工學院 開課系所︰材料系 考試日期（年月日）︰101.05.09 考試時限（分鐘）：10:20 ~ 13:00 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.Please describe in details how to synchronize the time clock in an inertial reference frame in special relativity.(5%) What is its difference from that in Newtonian Mechanics?(5%) Why?(5%) 2. (a) Please derive the kinetic energy K in special relativity.(10%) (b) Please derive the energy-momentum relation in relativity: E^2 = c^2p^2 + (m_0 c^2)^2. (5%) (c) Please show that a particle whose mass at rest is zero must travel with velocity equal to c. (5%) 3. (a) Show that for an extremely relativistic particle, the particle speed, u differs from the speed of light, c, Δu = c - u = (c/2)(m_0 c^2/E)^2, where m_0 is the rest mass and E is the energy. (10%) (b) Find Δu for electrons produced by 1) NSRRC in Hsinchu Science Park, Taiwan, where E = 1.5 GeV.(5%) 2) LHC in CERN, Switzerland, where E = 7000 GeV.(5%) 4.In an RC circuit as shown (a) Calculate the time constant. (b) Find the maximum charge on the capacitor during charging.(15%) R_1 ┌─/\/\/\─┬───┐ │ │ │ │ │ │ ● / ┴ C ε \ R_2 ┬ ● / │ │ \ │ │ │ │ └─────┴───┘ 5.Four particles form a square. The charges are q_1 = q_4 = Q and q_2 = q_3 = q (a) What is Q/q, if the net electrostatic force on particles 1 and 3 is zero? (b) Find the electric field at particle 2 by using Coulumb's law. (c) Find the electric field at particle 2 by using Gauss' law. (15%) ↑ │ q_1 │ q_2 ● │ ● │ │ │ ──────┼─────→x │ │ q_3 │ q_4 ●----┼----● │ a │ 6.Consider a cylindrical capacitor. The figure shows the cross section view. A cylindrical capacitor of length L formed by two coaxial cylinders of radii a and b, filled by two different dielectric materials with the dielectric constant κ_1 and κ_2 (see the figure). Assume L >> b, please calculate the capacitance. (15%) ┌───┬───┐ │ │ │ │ ┌─┴─┐ │ (請把它想像成圓形) │ │ a↑ │b │ │ │ └─┼→│ │ │ │ │ │ └─┬─┘ │ │ κ_1 │ κ_2 │ └───┴───┘ --

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