課程名稱︰普通物理學甲下 課程性質︰必修 課程教師︰趙治宇 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰2012/06/21 考試時限（分鐘）：10:20~11:10 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.The coil in Fig. 1 carries current I in the direction indicated, is parallel to an xz plane, has N turns and an area A, and lies in an uniform magnetic field B=Bx(i)+By(j)+Bz(k). What are (a)the orientation energy of the coil in the magnetic field and (b) the torque (in unit-vector notation) on the coil due to the magnetic field?(8%) Fig.1 坐標軸:+x:向右，+y:向上，+z:出紙面，在xz plane上有一個N匝的線圈， I方向：順時針 2.An infinitely long ideal solenoid has n turns per unit length and carries current i. Derive the magnetic field inside this solenoid (B=μ0 ni) from Biot-Savart law.(10%) 3.Fig.2 shows, in cross section, four thin wire that are parallel, straight,and very long. They carries identical current in the direction indicated. Initially all four wires are at distance d=15.0 cm from the origin of the coordinte system, where they creat a net magnetic field B (a) To what value of x must you move wire 1 along the x axis in order to rotate B counterclockwise by 30 degrees? (b) With wire 1 in that new position, to what value of x must you move wire 3 along the x axis to rotate B by 30 degrees back to its initial orientation?(8%) Fig.2 y │ ⊙4 │ │d d │ d ══⊙══════⊙═══x │ │d │ ⊕ │ │ 4. Fig.3 shows a rod of length L that is forced to move at a const speed v along horizontal rails. The rod, rails, and connecting strips at the right form a conducting loop. The rod has resistance Ω; the reat of the loop has negligible resistance. A current i through the long straight wire at distance 'a' from the loop set up a (non-uniform) magnetic field through the loop (a) What is the magnitude of the force that must be applied to the rod to make it move at const speed? (b) At what rate dose this force do work on the rod?(8%) Fig.3 x x x x x x x x x x x x x x x x x x x i x <-- ─────────── ˙ ˙ ˙ ˙ ˙ ˙ ˙ a ˙ ˙ ˙ ˙ ˙ ˙ ˙ ─────────┐ ˙ ˙ ˙ v│˙ ˙│ ˙ ˙ ˙<--│˙ B│ L ˙ ˙ ˙ ˙│˙ ˙│ ˙ ˙ ˙ ˙│˙ ˙│ ˙ ˙ ˙ ˙│˙ ˙│ ─────────┘ 5. A coil C of N turns is placed around a long solenoid S of radius R and n turns per unit length, as in Fig.4 (a) Show that mutual inductance for the coil-solenoid combination is given by M=μ0 π R^2 nN. (b) Explain why M does not depend on the shape,size, or possible lack of close packing of the coil.(8%) Fig.4 C ( □□□□□□ ( ( ( S ( (⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙ ( ( ( ( R ( ( ( (⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕⊕ ( ( ( ( □□□□□□( 6. For a series RLC circuit shown in Fig.5, the applied emf is ε=εm sin(ωd t) and the resulting current is i=I sin(ωd -ψ), where ωd is driving angular frequency, I is the current amplitude and ψ is the phase constant. (a) Derive current amplitude I and tanψ in terms of εm、R、L、C、ωd (b) Resonance of thus current occurs at ωd=? (8%) Fig.5 　→i ┌───-R-───┐ │ │ ε↑○ C ─ ↓i │ ─ │ │ └───-L-───┘ ← i 7. Using loop model to explain why the diamagnetic material is repelled from a region of great magnetic field toward a region of lesser field in a non-uniform field. (Hint: drawing are necessary for the answer of this problem) (8%) 8. The circuit in Fig.6 consists of switch S, an ideal battery with V, a resistor with R, and an air-filled capacitor. The capacitor has parallel circuit plates of radius r, separated by d. At time t=0, switch S is closed to begin charging the capacitor. The electric field between the plate is uniform. At t=ε0 π r^2 R/d, what is the magnetic field within the capacitor, at radial distance r/2? (Note: the permittivity is ε0 and the permeability constant is μ0) (8%) Fig.6 　 ┌───│ │──┐ │ │ ε↑○ ︴ │ ︴R │ │ └────V───┘ 9. Describe the behavior of electric field of (a) a partially polarized light, and (b) a circularly polarized light.(8%) 10. Describe the principle of Michelson's interferometer and its application. 11. In Fig.7,.7, two isotropic point sources of light(S1 and S2) are separated by distance 2.70μm along y axis and emit in phase at wavelength 900 nm and at the same amplitude. A light detector is located at point P at coordinate xp on the x axis. What is the greatst value of xp at which the detected light is mininum due to destructive inteference(8%) Fig.7 y │ │ ────˙────˙──x S1 │ P │ S2 ˙ │ 12. In a single-slit diffraction experiment, we could locate the mininum of the diffraction pattern on the screen through the equation: asinθ=mλ, where 'a' is the slit width and 'λ' represents the wavelength of the incident light. Derive the intensity of the pattern as a function of θ, which is I(θ)=Im (sinα/α)^2, where α=1/2ψ=πa/λ sinθ and Im represents the maximum intensity. You MUST use the vector method to solve this problem. (10%) --

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