課程名稱︰普通物理學甲
課程性質︰
課程教師︰張顏暉
開課系所︰電機系
考試時間︰2006/6/27
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試題 :
1. Assume that a electron of mass m and charge e moves in a circular orbit of
radius r about a nucleus. A magnetic field B is then applied perpendicular
to the plane of the orbit. Assuming also that the radius of the orbit does
not change and that the change in speed of the electron due to B is small,
find an expression for the change in magnetic moment of the electron due to
the field.(10)
2. In Fig.1, a laser beam of power 5W and diameter 2 mm is directed upward at
one circular face (of diameter d<2mm) of a perfectly reflecting cylinder.
the cylinder is lavitated because the upward radiation force matches the
downward gravitation force. If the cylinder's density is 1g/cm^3, what is
its height H.(10)
3. show that the simple magnifying lens has an angular magnification m_θ=
25cm/f, where f is the focal length (in cm) of the simple magnifier.(10)
4. Three EM wave travel through a certain point P along x-axis. They are
polarized parallel to the y-axis. With the following variation in their
amplitude. E1=(10.0mV/m)sin[(2.0x10^14 rad/s)t],
E2=( 5.0mV/m)sin[(2.0x10^14 rad/s)t+45度],
E3=(10.1mV/m)sin[(2.0x10^14 rad/s)t-30度].
Find the resultant electric field at P.(10)
5. A monochromatic beam of parallel light is incident on a "collimating" hole
of a diameter x>>λ. Point P lies in the geometric shadow region on a
distant screen. (see Fig.2 (a)). Two diffracting object, shown in Fig.2 (b),
are placed in turn over the collimating hole. Object A is an opaque circle
with a hole in it and B is the photographic negative of A. Using principle
of superposition show that the intensity at P identical for the two
diffracting object A and B.(10)
6. Show that the resolving power of a grating is given by R=Nm, where N is the
number of ruling in the grating and m is the order of diffraction. (Note for
N slit diffraction ( I(θ)=Im cos^2αsinNβ/Nsinβ, α=πasinθ/λ,
β=πdsinθ/λ, a is the slit width and d is the distant between adjacent
slits. Dispersion D=Δθ/Δλ)(10)
7. Write down the four Maxwell equations and explain the meaning of the
equations in common language (remember E and B are vectors and make sure
integral is a integrate around a surface or a circle). Write down the one
dimensional time independent Schrodinger equation for a particle of mass m
in a potential U(x). For the wavefunction ψ(x) with eigenenergy E write
down the time dependent wavefunction ψ(x,t). What is the probability of
finding the particle between x and x+dx.(10)
8. In a Compton scattering experiment, show that Δλ=h/mc(1-cosψ), where ψ
is the angle between the incoming photon and the scattered photon, and m is
the rest mass of the electron.(10)
9. Find the energy level of an electron in a rectangular quantum dots of size a
If there are a total of 12 electrons in the quantum dots, what is the total
energy of the electrons. (Dont forget that one electron has two spin states)
(10)
10. In a experiment similar to the Stern-Gerlach experiment shown in Fig.3, a
beam of unknown atoms was sent through a nonuniform magnetic field. If the
beam split into five parts after it passed through the B field, assume the
total spin of the atom is zero, what is the total orbital angular momentum
of the atoms? Assume the gradient of the magnetic field dB/dz=a, what is
the force acting on the atom when the atoms were passing through the
magnetic field? (In the answer please express μ_s,z in term of Bohr
magneton)(10)
11. Explain what are spontaneous emission, stimulated absorption and stimulated
emission. How to create a population inversion? Explain why the resonant
cavity could make the laser beam highly directional.(10)
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