課程名稱︰普通物理甲下 課程性質︰必修 課程教師︰王建萬 開課學院： 開課系所︰生工系 考試日期（年月日）︰2009/6/19 考試時限（分鐘）：110分鐘 是否需發放獎勵金：要 （如未明確表示，則不予發放） 試題 : 1. A plane electromagnetic wave, with wavelength 2.0m, travels in vacuum in the positive direction of an x axis. The electric field, of amplitude 500 V/m, oscillates parallel to the y axis. What are the (a) frequency, and (b) angular frequency, and (c) angular wave number of the wave? (d) What is the amplitude of the magnetic field component? (e) Parallel to which axis does the magnetic field oscillate? (f) What is the time-averaged rate of energy flow in watts per square meter associated with the wave? The wave uniformly illuminates a surface of area 4.0m^2. If the surface totally absorbs the wave, what are (g) the rate at which momentum is transferred to the surface and (f) the radiation pressure on the surface? (16%) 2.An ac generateor emf ε=εm*sin(Wd*t-π/4)，where εm = 20.0V and Wd = 500 rad/s.The current produced in a connect circuit is i(t) = I*sin(Wd*t-3π/4)，where I = 720 mA.At what time after t = 0 does (a)the generate emf first reach a maximum and (b)the current first reach a maximum ? (c)The circuit contains a single element other than the generate.Is it a capacitor，an inductor，or a resistor ? Justify your answer . (d)What is the value of the capacitance，inductance，or resistance，as the case may be ? (10%) 3.In a double-slit experiment, the electric fields of the waves arriving at point P on the screen are given by E1=E0Sin(kx1-wt),E2=E0Sin(kx2-wt), What are (a) the path difference,(b)the phase difference, and(c) the wave number difference of the two waves at P? What is the relation between d (slits separation),λ(wavelength), and θ if P shows (d) a bright fringe,(e) a dark fringe? see Fig.1 (11%) 4.In Fig.2，a capacitor with circular plates of radius R = 30.0cm is connected to a source of emf ε = εm*sinwt，where εm = 300V and w = 160 rad/s.The maximum value of the displacement current id=10.0μA.Neglect fringing of the electric field at the edges of the plates.(a)Whst is the maximum value of the current i in the circuit ? (b)What is the maximum value of dΦ/dt，where Φ is the electric flux through the region between the plates ? (c)What is the separation d between the plates ? (d)Find the maximum value of the magnitude of B between the plates at a distance r = 20.0am from the center ? (10%) 5.Fig.3 show a cross section across a diameter of a long cylindrical conductor of radius a = 4.00cm carrying uniform current 300 A.What is the magnitude of the current's magnetic field at radial distance(a)0，(b)2.00cm，(c)4.00cm (wire's surface)，and(d)6.00cm ? (10%) 6.The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern.(Fig.4)(a)Show that the intensity drops to one-half the maximum value when (sinα)^2 = α^2/2. (b)Verify that α = 1.39 rad is a solution to the transcendental equation of (a).(c)Show that the FWHM is Δθ= 2sin-1(0.443λ/a)，where a is the slit width.Calculate the FWHM of the central maximum for slit width(d)1.50λ， (e)2.50λ，and(f)6.00λ (12%) 7.Fig.5 show a rod of length L = 16.0cm that is force to move at constant speed v = 10.00m/s along horizontal rails.The rod，rails，and connecting strip at right form a conducting loop.The rod has a resistance 0.600Ω；the rest of the loop has negligible restance A current i = 160a through the long straight wire at distance a = 12.0mm from the loop sets up a (nonuniform) magnetic field through the loop.Find the (a)emf and (b)current induced in the loop.(c)At what rate is thermal energy generated in the rod ? (d)What is the magnitude of the force that must applied to the rod to make it move at constant speed ? (e)At what rate does this force do work on the rod ? (11%) 8.In Fig.6, a wire loop of dimensions L=60.0cm and W=40.0cm lies in a magnetic field B. What are the (a) magnitude ε and (b) direction (clockwise or counterclockwise - or "none" if ε=0) of the emf induced in the loop if B=(6.00×10^-2T/m)yk? What are (c) ε and (d) the direction if B=(8.00×10^-2T/s)tk? What are (e) ε and (f) the direction if B=(12.00×10^-2T/m‧s)tk? What are (g) ε and (h) the direction if B=(5.00×10^-2T/m‧s)xtj? What are (i) ε and (j) the direction if B=(8.00×10^-2T/m‧s)yti? (20%) Halliday 8th Fundamentals of PHYSICS Extended 1. 33.25 2. 31.33 3. 4. 32.29 5. 29.45 6. 36.17 7. 30.35 8. 30.18 Figure 1 35-10 Figure 2 32-26 Figure 3 29-70 Figure 4 36-8(b) Figure 5 30-59 Figure 6 30-49 -- 建萬爺 就甘心 --

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