課程名稱︰普通物理學乙
課程性質︰必修
課程教師︰王建萬
開課學院：
開課系所︰農化系
考試日期（年月日）︰2012.6.20
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. A plane electromagnetic wave, with wavelength 2.50m, travels in vacuum
in the direction of an x axis. The electric field, of amplitude 350 V/m,
oscillates parallel to the y axis. What are the (a) frequency, (b) angular
frequency, and (c) angular wave number of the wave? (d) what is the
amplitude of the magnetic field component? (e) Parallel to which axos does
the magnetic field wscillate? (f) What is the time averaged rate of energy
flow in watts per square meter associated with this wave? The wave
uniformly illuminates a furface of 2.40m^2. If the furface totally absorbs
the wave, what are (g) the rate at which momentum is transferred to the
surface and (h) the radiation pressure on the surface?
2. In Fig.1 (Holiday第九版 Fig.35-38) , two isotropic point sources S1 and S2
emit light in phase at wavelength λ and at same amplitude. The sources
are separated by distance 2d=5.00λ. They lie on an axis that is parallel
to an x axis,which runs along a viewing screen at distance D=30.0λ.
The origin lies on the perpendicular bisector between the sources. The
figure shows two rays reaching point P on the screen, at position Xp.
(a) At what valur of Xp do the rays have the minimum phase difference?
(b) What multiple of λ gives that minimum phase difference? (c) At what
value of Xp do the rays have the maximum possible phase difference?
What multiple of λ gives (d) that maximum phase difference and (e) the
phase difference when Xp=6.00λ? (f) When Xp=6.00λ, is the resulting
intensity at point P maximum, minimum, intermediate but closer to maximum,
or intermediate but closer to minimum?
3. The full width at half-maximum (FWHM) of a central diffraction maximum is
defined as the angle between the two points in the pattern.(See Fig.2)
(課本Fig.36-8) (a) Show that the intensity drops to one-half the maximum
value when (sinα)^2=α^2/2. (b) Verify that α=1.39rad(80°) is a
solutionto the transcendental equation of (a) . (c) Show that the FWHM is
△θ=2(sin)^-1 (0.443λ/a), where a is the slit width. Calculate the
FWHM of the central maximum for slit width (d) 1.00λ (e) 5.00λ
(f) 8.00λ.
4. Fig.3 (課本Fig31-35) shows an ac generator connected to a 'black box'
through a pair of terminals. The box contains an RLC circuit, possibly
even a multiloop circuit, whose elements and cinnections we do not know.
Measurements outside the box reveal that ε(t)=(100.V)sinωdt and
i(t)=(1.40A)sin(ωdt+42.0°). (a) What is the power factor? (b) Does the
current lead or lag the emf? (c) Is the circuit in the box largely
inductive or largely capacitive? (d) Is the cirvuit in the box in
resonance? (e) Must there be a capacitor in the box? (f) An inductor?
(g) A resistor? (h) At what average rate is the energy delivered to the
box by the generator? (i) Why do not you need to know ωd to answer all
these questions?
5. Fig.4a (課本Fig.32-34) shows the vurrent i that is produced in a wire of
resistivity 1.84x10^-8Ω.m.The magnitude of the current versus t is shown
in Fig.4b. The vertical axis scale is set by Is=12.5A, and the horizontal
axis scale is set by ts=60.0ms. Point P is at radial distance 1.20cm from
the wire's center. Determine the magnitude of the magnetic field Bi at
point P due to the actual current i in the wire at (a) t=24.0ms,
(b) t=48.0ms, and (c) t=72.0ms. Next, assume that the electri field
driving the current is confined to the wire. Then determine the magnitude
of the magnetic field Bid at point P due to the dicplacement current Id in
the wire at (d) t=24.0ms, (e) t=48.0ms, (f) t=72.0ms. At point P at t=10.0s
what is the direction (into or out of the page) of (g) Bi, (h) Bid.
6. Fig.5 (課本Fig.29-87) shows a cross section of a long conducting coaxial
cable and gives its radii (a,b,c). Equal but opposite currents i are
uniformly distributed in the two cinductors. Derive expressions for B(r)
with radial distance r in the ranges (a)r<c, (b) c<r<b, (c) b<r<a,
(d) r<a. Assume that a=2.00cm, b=1.60cm, c=0.40cm, i=160A. Calculate B(r)
at (e) r=2.40cm (f) r=1.80cm, (g) r=0.
7. The conducting rodshown in Fig.6 (課本Fig.30-50) has length L and is being
pulled along horozontal, frictionless cinducting rails at a constant
velocity v. The rails are cinnected at one end with a metal strip. A uniform
magnetic field B, directed out of the page, fills the region in which the
rod moves. Assume that L=16.0cm, v=5.00m/s, and B=1.60T. What are the (a)
magnitude and (b) direction (up or down the page)of the wmf induced in the
rod? What are the (c) size and (d) direction of the current in the
conducting loop? Assume that the resistance of the rod is 0.600Ω and that
the resistance of the rails and metal strip is negligibly small. (e) At
what rate is the thermal energy being generated in the rod? (f) What
external force on the rod is needed to maintain v? (g) At what rate does
this force do work on the rod?
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