※ [本文轉錄自 NTU-Exam 看板] 作者: amnotu (白告) 看板: NTU-Exam 標題: [試題] 94下 趙治宇 普通物理學甲下 期末考 時間: Wed Jun 28 02:30:25 2006 課程名稱︰普通物理學甲下 課程性質︰化工系定必修 課程教師︰趙治宇 開課系所︰物理系 考試時間︰2006/06/27 10:20~13:10 是否需發放獎勵金：是　謝謝 （如未明確表示，則不予發放） 試題 : Do all problems in detail, full points 100. Good luck! 1. In unit-vector notation, what is the magnetic field at point P in Fig.1 if i=10 A and a= 8.0 cm? (Note that the wires are not long.) (8 pts) 2. Fig.2 shows a cross section of a hollow cylindrical conductor of radii a and b, carrying a uniformly distributed current i. (a) Show that the magnetic field magnitude B(r) for the radial distance r in the range b < r < a is given by B=((μ0i)/2π(a^2-b^2))*((r^2-b^2)/r) (3 pts) (b) Show that when r= a, this equation gives the magnetic field magnitude B at the surface of a long straight wire carrying current i; when r= b, it gives zero magnetic field; and when b=0, it gives the magnetic field inside a solid conductor of radius a carrying current i (3 pts) (c) Assume that a= 2.0 cm, b= 1.8 cm, and i= 100 A, and then plot B(r) for the range 0 < r <6 cm. 3. Fig.3 shows a coil of N2 turns wound as shown around part a toroid of N1 turns. The toroid's inner radius is a, its outer radius is b, and its height is h. Show that the mutual inductance M for the toroid-coil combination is given by M=(μ0*N1*N2*h/2π)*ln(b/a) (10 pts) 4. In an oscillating series RLC circuit, show that ΔU/U, the fraction of the energy lost per cycle of oscillation, is given to a close approximation by 2πR/ωL, The quantity ωL/R is often called the Q of the circuit(for quality). A high-Q circuit has low resistance and a low fractional energy loss(=2π/Q) per cycle. (8 pts) 5. A parallel-plate capacitor with circular plates of radius R is being discharged. The displacement current through a central circular area, parallel to the plates and with radius R/2, is 2.0 A. What is the discharging current? (8 pts) 6. A beam of partially polarized light can be considered to be a mixture of polarized and unpolarized light. Suppose we send such a beam through a polarizing filter and then rotate the filter through 360° while keeping it perpendicular to the beam. If the transmitted intensity varies by a factor of 5.0 during the rotation, what fraction of the original beam is associated with the beam's polarized light? (8 pts) 7. Fig. 7a shows a lens with radius of curvature R lying on a flat glass plate and illuminated from above by light with wavelength λ. Fig 7b (a photograph taken from above the lens) shows that circular interference fringes (called Newton's rings) appear, associated with the variable thickness d of the air film between the lens and the plate. Find the radii r of the interference maxima assuming r/R << 1. (8 pts) 8. Derive this expression for the intensity pattern for a three-slit "grating" I= 1/9 Im(1+4cosφ+4cos^2φ), where φ= (2πd sinθ)/λ and a << λ. (8 pts) 9. Describe the working principle of near-field optical microscope. (8 pts) 10. Describe thr working principle of recording and playback head for tape. (8 pts) 11. Describe why Gecko's toes have strong adhesion force on any rough surface? (6 pts) 12. Using classical model to explain the discovery of diamagnetic material. (10 pts) Figure 1,2,3,7a,7b來自於Fundamentals of Physics, Halliday 7th. 1.p.790, Fig.29-83 2.p.790, Fig.29-87 3.p.824, Fig.30-78 7a.p.985, Fig.35-46(a) 7b.p.985, Fig.35-46(b) --

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