7. The electric field in a region of space has the components E_y = E_z = Q and E_x = 4.00x (N/C). Point A is on thej; axis at y = 3.00 m, and point B is on the x axis at x = 4.00 m. What is the potential difference V_B - V_A?

8. Three charges of +0.1 C each are placed on the corners of an equilateral triangle, 1.0 m on a side. If energy is supplied at the rate of 1.0 KW, how many hours would be required to move one of the charges onto the midpoint of the line joining the other two?

9. Figure 1 shows a wood cylinder of mass m = 0.25 kg and length L =0.10 m, with N = 10 turns of wire wrapped around it longitudinally, so that the plane of the wire coil contains the long central axis of the cylinder. The cylinder is released on a plane inclined at an angle 6 to the horizontal, with the plane of the coil parallel to the incline plane. If there is a vertical uniform magnetic field of magnitude B = 0.50 T, what is the least current I through the coil that keeps the cylinder from rolling down the plane?

10. A stationary, circular wall clock has a face with a radius of 20 cm. Six turns of wire are wound around its perimeter; the wire carries a current 2.0 Ain the clockwise sense. The clock is located where there is a constant, uniform external magnetic field of 50 mT(but the clock still keeps perfect time). At exactly 1:00 p.m., the hour hand of the clock points in the direction of the external magnetic field. After how many minutes will the minute hand point in the direction of the torque on the winding due to the magnetic field?

11. Atom 1 of mass m\ and atom 2 of mass nn are both singly ionized with a charge of +q. After being introduced into a mass spectrometer and accelerated from rest through a potential difference V, each ion follows a semicircular path in a uniform magnetic field of magnitude B. What is the distance Ax between the points where the ions strike the detector?

12. One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area 1.20x10-3 m2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 12.0 . If an externally applied uniform longitudinal magnetic field in the core changes from 1.60 T in one direction to 1.60 T in the opposite direction, how much charge flows through a point in the circuit during the change?

13. A pendulum consisting of a 0.01 kg mass is suspended from a string 0.1 m in length. Let the amplitude of its oscillation be such that the string in its extreme positions makes an angle of 11°(cosll° = 0.98) with the vertical. If its energy is quantized, what is the quantum number n (to the nearest order of magnitude)? (g = 10 m/s2) (According to this result, the quantized nature of the energy of the oscillations will not be apparent for large-scale system )

14. In a photoelectric experiment in which a sodium surface is used, one finds the maximum kinetic energy of photoelectrons is 0.62 eV for a wavelength of 4000 人，find the cutoff wavelength for sodium?

15. Consider an electron confined by electrical forces to move between two rigid “walls” separated by 1.5 A. What is the quantized energy value for the lowest stationary state?

二、問答計算題(共70分） 1.在推導氣體動力論巨觀現象與微觀行為關係式時，我們常用正立方體密閉容器當 例子。若有學生詢問其他形狀密閉容器是否適用相同關係式，你會如何回答並舉 例推導說明？（5%)

2.在推導單狹縫繞射關係式時，若有學生將狹缝視為無窮多點光源，並假設狹縫兩 端點光源到光屏上P點之光程差為2λ，之後將狹縫分成等大小的A、B兩區，因 這兩區的點光源皆對應相差1λ的光程差，為相長干涉。故學生推論光屏上P點為 亮紋，請問你會如何更正該學生的錯誤？（5%)

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