課程名稱︰普通物理學甲下 課程性質︰共同必修 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）︰2008/6/20 考試時限（分鐘）: 110分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 08S Mid Term Exam 1.An ac generateor emf ε=εm*sin(Wd*t-π/4)，where εm = 40.0V and Wd = 400 rad/s.The current produced in a connect circuit is i(t) = I*sin(Wd*t-3π/4)，where I = 680 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%) 2.A plane electromagnetic wave，with wavelength 4.0m，travels in vacuum in the positive direction of an x axis.The electric field，of amplitude 400 V/m， oscillates parallel to the y axis.What are the (a)frequence， (b)angular frequence，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 energe flow in watts per square meter associated with this wave ? The wave uniformly illuminates a surface of area 3.0m^2.If the aurface totally absorbs the wave，what are (g)the rate at which momentum is transferred to the surface and (h)the radiation preaaure on the surface ? (16%) 3.In a double-slit experiment，the electric field of the waves arriving at point P on the screen are given by E = (300μV/m)*sin[(1.4*10^15)t] E = (300μV/m)*sin[(1.4*10^15)t + 50.0 rad]， where time t is in seconds.(a)What is the amplitude of the resultant electric field at point P ? (b)What is the ratio of the Ip at point P to the intensity Icen at the center of the interference psttern ?(c)Describ where point P is in the interference pattern by giving the maximum or minimum on which is lies.In a phasor diagram of the electric fields，(d)at what rate would the phasors rotate around the origin and (e)what is the angle between the phasors ? (11%) 4.Fig.1 show a cross section across a diameter of a long cylindrical conductor of radius a = 3.00cm carrying uniform current 200 A.What is the magnitude of the current's magnetic field at radial distance(a)0，(b)1.00cm，(c)3.00cm (wire's surface)，and(d)6.00cm ? (10%) 5.In Fig.2，a capacitor with circular plates of radius R = 24.0cm is connected to a source of emf ε = εm*sinwt，where εm = 220V 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 = 30.0am from the center ? (10%) 6.Fig.3 show a rod of length L = 10.0cm that is force to move at constant speed v = 8.00m/s along horizontal rails.The rod，rails，and connecting strip at right form a conducting loop.The rod has a resistance 0.300Ω；the rest of the loop has negligible restance A current i = 120a through the long straight wire at distance a = 10.0mm 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%) 7.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)1.00λ， (e)4.00λ，and(f)8.00. (12%) 8.In Fig.5，a wire loop of dimensions L = 50.0cm and W = 30.0cm lies in a magnetic field B.What are the (a) magnitude ε and (b) direction(clockwise or counterclockwise-or "non" if ε = 0) of the emf induced on the loop if B = (5.00*10^-2T/m)yk ? What are (c) ε and (d) the direction if B = (10.0*10^-2T/ms)xtj ? What are (i) ε and (j) the dirrection if B = (5.00*10^-2T/ms)yti ? (20%) Find，，，， 圖參考課本HALLIDAY 8TH Fig.1 = Fig.29-70 Fig.2 = Fig.32-36 Fig.3 = Fig.30-59 Fig.4 = Fig.36-8(b) Fig.5 = Fig.30-49 --

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