課程名稱︰普通物理下
課程性質︰大一下必修
課程教師︰蔡爾成
開課系所︰電機系
考試時間︰2005/6/23
試題 :
1.A sodium light source moves in a horizontal circle at a constant speed of
0.100c while emitting light at the proper length wavelength of
λο = 589.00nm. Wavelength is measured for that light by a detector fixed at
the center of the circle. What is the wavelength shift λ－λο?
2.Derive the expression △θhw = λ/(N*d*cosθ) for the half-width of lines in
a grating's diffraction pattern.
3.Slits of unequal widths are used in a double-slit arrangement to produce an
interference pattern on a distant screen. If only the narrower slit 1 is
illuminated (the wilder slit 2 is covered), the light reaching the center of
the pattern has amplitude Eο and intensity Iο. If only slit 2 is
illuminated, the amplitude of light reaching the pattern center is 2Eο. When
both slits are illuminated and a two slits interference pattern is on the
screen, what is the intensity I(θ) in the pattern as a function of angle θ?
4.A short straight object of length L lies along the central axis of a
spherical mirror, a distance p from the mirror. Show that its image in the
mirror has a length L', where L' = L*(f/(p - f))^2.
5.Show that the fractional half-width of a resonance curve for an RLC circuit
is given by △ωd/ωο = R*(3C/L)^0.5 in which ωο is the angular frequency
at resonance and △ωd is the width of the resonance curve at half-amplitude.
6.Assume frame S' moves with velocity v relative to frame S. Derive the
relativistic velocity transformation equation u = (u' + v )/(1 + u'v/c^2)
where u' is the velocity measured in the S' and u is the velocity measured in
the frame S.(All velocities are along the x-axis.)
7.We may describe a device in an alternating-current circuit by complex current
I = Iο*e^(iωt) and complex voltage V = Vο*e^(iωt). The physical current i
for the device is the real part of the corresponding complex current,
i = Re(I). similarly, the physical voltage v for the device is the real part
of the corresponding complex voltage, v = Re(V). Show that the average rate
at which energy is dissipated for a device in an alternating-current circuit
can be written as Pavg = 0.5*RE(IV*) where I and V are the complex current
and complex voltage drop across the device.
8.The complex impedance is defined as the ratio of complex potential over
complex current for a device in an alternating circuit. Prove the complex
impedance for capacitor C is 1/(jωC) and complex impedance for inductor L is
jωL, where j = ( －1 )^0.5.
9.What must be the magnitude of a uniform eletric field if it is to have the
same energy density as that possessed by a 1.00T magnetic field?
10.Show that the following plane traveling electromagnetic wave along the z
→ ^ → ^
axis E = Eo*sin(ωt － kz)i B = Bo*sin(ωt － kz)j is a solution to the
Maxwell equations in free space and its wave speed
c = ω/k = 1/(μο*εο)^0.5.
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