課程名稱︰普通物理學甲下
課程性質︰必修
課程教師︰蔡爾成
開課學院：理學院
開課系所︰大氣系
考試日期（年月日）︰2011/06/21
考試時限（分鐘）：120分鐘
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
→
1.[10%] A uniform magnetic field B is perpendicular to the plane of a circular
wire loop of radius r. The magnitude of the field varies with time according
to B = Bo*e^(-t/τ), where Bo and τ are constants. Find an expression for
the emf in the loop as a function of time.
2.[10%] In an oscillation series RLC circuit, show that ΔU/U, the fraction of
the energy lost per cycle of oscillation, is given to a close approximation
by 2πR/ωL.
3.The magnetic field of Earth can be approximated as the magnetic field of a
dipole. The horizontal and vertical components of this field at any distance
r from Earth's center are given by
μoμ μoμ
B = ──── cosλ , B = ──── sinλ ,
h 4πr^3 m v 2πr^3 m
where λ is the magnetic latitude (this type of latitude is measure from
m
the geomagnetic equation toward the north or south geomagnetic pole). Assume
that Earth's magnetic dipole moment has magnitude μ = 8.00*10^22 A*m^2.
(a)[5%] Show that the magnitude of Earth's field at latitude λ is given by
___________ m
μoμ / 2
B = ──── / 1+3sin λ .
4πr^3 V m
(b)[5%] Show that the inclination φi of the magnetic field is related to
the magnetic latitude λ by tanφi = 2tanλ .
m m
4.[10%] In Fig. 33-42, unpolarized light is sent into a system of three
polarizing sheets. The angles θ1, θ2, and θ3 of the polarizing directions
are measured counterclockwise from the positive direction of the y axis
(they are not drawn to scale). Angles θ1 and θ3 are fixed, but angle θ2
can be varied. Figure 33-43 gives the intensity of the light emerging from
sheet 3 as a function of θ2. (The scale of the intensity axis is not
indicated.) What percentage of the light's initial intensity is transmitted
o
by the system when θ2 = 30 ? (課本有圖)
5.[10%](37-21) If m is a particle's mass, p is its momentum magnitude, and K
is its kinetic energy, show that
(pc)^2 - K^2
m = ──────── . (考卷上此題並無附圖)
2Kc^2
6.[10%] Two different surfaces S1 and S2 have the same boundary. Prove that
the sum of current i and displacement current i passing through these two
d
surfaces are the same. i + i = i + i .
1 d1 2 d2
7.[10%] We may describe a device in an alternating-current circuit by complex
__
current I = Io*e^(jωt) and complex voltage V = Vo*e^(jωt), where j = v-1.
The physical current i for the device is the real part of the corresponding
complex current, i = Re(I). Similar, the physical voltage v for the device
is the real part of the corresponding complex voltage, v = Re(V). The
V
complex impedance Z = ── is defined as the ratio of complex potential over
I
complex current for a device in an alternating circuit. Prove the complex
1
impedance for capacitor C is ─── and the complex impedance for inductor
jωC
L is jωL.
8.[10%] What are the four Maxwell equations in both integral and differential
forms?
9.[10%] For a plane traveling electromagnetic wave along the x axis with the
eletric field
→ → ^
E (x , t) = Eo*cos(ωt-kx)j
where
ω 1
── = ───── ,
────
k V μoεo
→ →
what is the magnetic field B (x , t)?
10.[10%] If two events (t1, x1), (t2, x2) occur at the same space point
x1 = x2 but at different times t1 ≠ t2, show that it is impossible to find
another inertial frame in which these two events occur simultaneously under
special relativity.
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