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◆ From: 220.129.90.63
課程名稱︰普通物理甲
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）︰2007/06/21
考試時限（分鐘）：三小時
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Figure A shows a wire of ring of radius a = 1.8cm that is perpendicular to
the general direction of a radailly symmetric, diverging magnetic field. The
magnetic field at the ring is everywhere of the same magnitude B = 3.4mT,
and its direction at the ring everywhere makes an angle θ = 20degree normal
to the plane of the ring. The twisted lead wires have no effect on the
problem. Find the magnitude of the force the field exerts on the ring if the
ring carries a current i = 4.6mA. (10pts)
2.Figure B shows a cross section of a lobg thin ribbon of width w = 4.91cm that
is carrying a uniformly distributed total current i = 4.61μA into the page.
In unit-vector notation, what is the magnitude B at a point P in the plane of
the ribbon at a distance d = 2.16cm from its edge? (10pts)
3.Assume that an electron of mass m and charge magnitude e moves in a circular
orbit of radius r about a nucleus . A uniform magnetic field B is the
established perpendicular to the plane of the orbit. Assuming also that the
radius of the orbit does not change and that the change in the speed of the
electron due to field B is small, find an expression for the change in the
orbital magnitude dipole moment of the electron due to the field. (10pts)
4.In figure C, R1 = 8.0Ω, R2 = 10Ω, L1 = 0.30H, L2 = 0.20H, and the ideal
battery has ε = 6.0V.
(a)Just after switch S is closed, at what rate is the current in inductor 1
changing? (5pts)
(b)When the circuit is in steady state, what is the current in inductor 1?
(5pts)
5.A parallel-plate capacitor with circular plates of radius R = 16mm and gap
width d = 5.0mm has a uniform electric field between the plates. Starting at
time t = 0, the potential difference between the plates is V = 100Ve^(-t/τ)
where the time constant τ = 12ms. At radial distance r = 0.80R from the
central axis, what is the magnitude field magnitude
(a)As a function of time for t≧0? (8pts)
(b)At time t = 3τ? (2pts)
6.Figure D depicts a simplistic optical fiber: a plastic core (n1 = 1.58) is
surrounded by a plastic sheath (n2 = 1.53). A light ray is incident on one
end of the fiber at angle θ. The ray is to undergo total internal
reflection at point A, where it encounters the core-sheath boundary. (Thus
there is no loss of light through that boundary.) What is the maxium value
of θ that allows total internal reflection at A? (10pts)
7.Figure E shows a coil of N2 turns would as shown around part of a toroid of
N1 turns. The toroid's inner radius is a, its outer radius is b, and its
height is h. Shows that the mutual inductance M for the toroid-coil
combination is given by M = (μ0N1N2h/2π)㏑(b/a). (10pts)
8.Describe the principle and application of Michelson's interferometer? (10pts)
9.
(a)What is the angular seperation of two stars if their images are barely
resolved by the Thaw refracting telescope at the Allegheny Observatory in
Pittsburgh? The lens diameter is 76cm and its focal length os 14m. Assume
λ = 550nm. (3pts)
(b)Find the distance between these barely resolved stars if each of them is 10
light-years from earth. (3pts)
(c)For the image of a single star in this telescope, find the diameter of the
first dark ring in the diffraction pattern, as measured on a photographic
plate placed at the focal plane of the telescopic lens. Assume that the
structure of the image is associated entirely wuth diffraction at the lens
aperture and not wiyh lens "errors". (4pts)
10.An alternating source with a variable frequency, a capacitor with
capacitance C, and a resistor with resistance R are connected in series.
Figure F gives the impedance Z of the circuit versus the driving angular
frequency ωd; the curve reaches an asymptote of 500Ω. The figure also
gives the reactance Xc for the capacitor versus ωd. What are
(a)R? (5pts)
(b)C? (5pts)
所有圖片均來自Halladay/Resnick/Walker所著之Fundamentals of Physics, edition 7
Fig. A : p.760 Fig. 28-42
Fig. B : p.784 Fig. 29-51
Fig. C : p.825 Fig. 30-83
Fig. D : p.919 Fig. 33-59
Fig. E : p.824 Fig. 30-78
Fig. F : p.856 Fig. 31-27
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