課程名稱︰普通物理學甲下 課程性質︰大一必修 課程教師︰李慶德 開課學院：電資學院 開課系所︰電機工程學系 考試日期（年月日）︰2015/06/25 考試時限（分鐘）：110分鐘 試題 : =============================================================================== General Physics A ─ Final Exam June 25, 2015 Useful Info and Formulas: → ^ → μ0 i ds x r ◎ The Biot-Savart law: dB = ── ───── 4π 2 r -12 2 2 ◎ Permittivity constant: ε0 = 8.85 x 10 C /N m . -7 ◎ Permiability constant: μ0 = 4π x 10 T m /A. -19 ◎ Elementary or fundamental charge: e = 1.602 x 10 C. → → ◎ Current density and drift velocity: J = ne Vd, where the product ne is carrier charge density. 2 1 2 q ◎ Eletric energy stored in a capacitor: UE = ─CV = ── 2 2C 1 2 ◎ Magnetic energy stored in an inductor: UB = ─L i 2 2 B ◎ The energy density in the magnetic field: uB = ─── 2μ0 ◎ Capacitive and inductive reactances under the driving emf ξ=ξm sin( wd t ) are given by Xc = 1 / (wd C) and XL = wd L, respectively. → → d → → ◎ The Faraday law of induction: ∮E．ds = - ─∫B．dA. dt → → d → → ◎ The Ampere-Maxwell law: ∮B．ds = μ0 i_enc + μ0 ε0 ─∫E．dA. dt → 1 → → ◎ The Poynting vector: S = ── E x B μ0 ◎ When an object gains an energy △U from a beam of electromagnetic radiation during normal incidence, its momentum change △p is given by: △U △p = (1 + f)──, where f = 0 for total absorption and f = 1 for total c reflection. I. Calculation Problems: (prob.14[15%] & prob.15[20%]) 14. [15 points] As a parallel-plate capacitor with circular plates 20 cm in diameter is being charged, the current density of the displacement current 2 in the region between the plates is uniform and has a magnitude of 20 A/m . (a) Calculate dE/dt in this region. (b) Calculate the magnitude B of the magnetic field at a distance r = 50mm from the axis of symmetry of this region. (c) Calculate the magnitude B of the megnetic field at a distance r = 30cm from the axis of symmetry of this region. 15. [20 points] A plane electromagnetic wave traveling in the positvie direction of an z-axis in vacuum has electric field component → ^ E = Em sin(kz - wt) i, where k = w/c. Assume that Em = 1.2 V/m and 15 w = 1.6π x 10 /s. (a) What is the magnetic field component of this eletromagnetic wave? Express it(properly in the vector notaion) in terms of Em, etc. (b) Calculate the intensity of this electromagnetic radiation. (c) If this electromagnetic radiation is intercepted and totally reflected by a surface perpendicular to the z-axis, find the radiation pressure on the surface. → ^ (d) if, instead of E = Em sin(kz - wt)i, the eletric field component is → ^ given by E = Em sin(kz + wt)i and everything else stays the same, what are the traveling direction and the magnetic component of the electromagnetic wave? II. Multiple-choice Problems: (problems 1-13, 5 points each) → → 1. An electron enters a region of uniform perpendicular E and B fields. It is → observed that the velocity v of the electron is unaffected. A possible explanation is: → → (A) v is parallel to E and has magnitude E/B → → (B) v is parallel to B → → → (C) v is perpendicular to both E and B and has magnitude B/E → → → (D) v is perpendicular to both E and B and has magnitude E/B (E) the given situation is impossible 2. The current is from left to right in the conductor shown. The magnetic field is into the page and point S is at a higher potential than point T. The charge carriers are: Fig: (A) positive (B) negative (C) neutral (D) absent (E) moving near the speed of light 3. Two long straight wires parallel and carry current in opposite directions. The currents are 8.0 A and 12 A and the wires are seperated by 0.40 cm. The magnetic field at a point midway between the wires is: (A) 0 T -4 (B) 4.0 x 10 T -4 (C) 8.0 x 10 T -4 (D) 12 x 10 T -4 (E) 20 x 10 T 4. A square loop of wire lies in the plane of the page and carries a current → I as shown. There is a uniform magnetic field B directed towards the top of the page, as indicated. The loop will tend to rotate: Fig: (A) about PQ with KL coming out of the page (B) about PQ with KL going into the page (C) about RS with MK coming out of the page (D) about RS with MK going into the page (E) about an axis perpendicular to the page 5. A hollow cylindrical conductor(inner radius = a, outer radius = b) carries a current i uniformly spread over its cross section. Which graph below correctly gives B as a function of the distance r from the center of the cylinder? (A) I, Fig: (B) II, Fig: (C) III, Fig: (D) IV, Fig: (E) V, Fig: 6. A rectangular loop of wire is placed perpendicular to a uniform magnetic field and then spun around one of its sides at frequency f. The induced emf is a maximum when: (A) the flux is zero (B) the flux is a maximum (C) the flux is half its maximum value (D) the derivative of the flux with respect to time is zero (E) none of the above 7. One hundred turns of insulated copper wire are wrapped around an iron core 2 of cross-sectional area 0.100 m . The circuit is completed by connecting the coil to a 10 Ω resistor. As the magnetic field along the coil axis changes from 1.00 T in one direction to 1.00 T in the other direction, the total charge that flows through the resistor is: (A) 0.01 C (B) 0.02 C (C) 0.2 C (D) 1 C (E) 2 C 8. An LC circuit consists of a 1 μF capacitor and a 4 mH inductor. Its oscillation frequency is approximately: (A) 0.025 Hz (B) 25 Hz (C) 60 Hz (D) 2500 Hz (E) 16,000 Hz 9. In an RLC series circuit, which is connected to a source of emf εm cos( wt ), the current lags the voltage by 45° if: (A) R = 1/wC - wL (B) R = 1/wL - wC (C) R = wL - 1/wC (D) R = wC - 1/wL (E) wL = 1/wC 10. Suppose you are looking into one end of a long cylindrical tube in which there is a uniform electric field, pointing away from you. If the magnitude of the field is decreasing with time the direction of the induced magnetic field is: (A) toward you (B) away from you (C) clockwise (D) counterclockwise (E) to your right 11. Two of Maxwell's equations contain a path integral on the left side and an area integral on the right suppose the area is the surface of a piece of → paper at which you are looking and dA is chosen to point toward you. Then, the path integral is: (A) clockwise around the circumference of the paper (B) counterclockwise around the circumference of the paper (C) from left to right (D) from right to left (E) from top to bottom 12. Select the correct statement: (A) ultraviolet light has a longer wavelength than infrared (B) blue light has a higher frequency than X rays (C) radio waves have a higher frequency than gamma rays (D) gamma rays have a higher frequency than infrared waves (E) electrons are a type of electromagnetic wave 2 13. Light with an intensity of 1kW/m falls normally on a surface with an 2 area of 1 cm and is completely reflected. The force of the radiation on the surface is: -11 (A) 3.3 x 10 N -10 (B) 1.7 x 10 N -10 (C) 3.3 x 10 N -10 (D) 6.7 x 10 N -4 (E) 1.0 x 10 N ================================== 試題完 =================================== 備註： 1. 可帶計算機 2. 圖片待補 --

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