※ [本文轉錄自 NTU-Exam 看板]
作者: ultimatePTT (終極俊) 看板: NTU-Exam
標題: [試題] 94下 蔡爾成 普通物理學甲 期末考
時間: Mon Jun 26 17:19:53 2006
課程名稱︰普通物理學甲下
課程性質︰系定必修
課程教師︰蔡爾成
開課系所︰大氣系
考試時間︰95/06/26
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. [10%] Show that the magnitude of the static magnetic field produced at the
center of a rectangular loop of wire of length L and width W, carrying a
current i, is 1/2
2μoi (L^2 + W^2)
B = ─── ───────
π LW
2. (a) [5%] Two inductors L and L are connected in parallel, show that the
1 2
equivalent inductance is given by 1 1 1
─── = ── + ──
L L L
eq 1 2
(b) [5%] Why must the separation of these two inductors be large for the
above relationship to hold?
3. [10%] In an oscillating RLC circuit, show that the fraction of the energy
lost per cycle of oscillation, ΔU/U, is given to a close approximation
by 2πR/ωL.
4. [10%] Prove that the displacement current in a parallel-plate capacitor of
capacitance C can be written as i = C(dV/dt), where V is the potential
d
difference between the plates.
5. [10%] 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?
6. [10%] By macking use of the example of a solenoid, show that the energy
density of the static magnetic field is 1 2
U = ── B
B 2μo
7. [10%] The complex impedance is defined as the ratio of complex potencial
over complex current for a device in an alternating circuit. Prove the
complex impedance for capacitor C is 1/jωC and the complex impedance for
inductor L is jωL, where j = (-1)^1/2.
8. [10%] Prove that the speed of the Electromagnetic wave c = (μoεo)^(-1/2)
by giving an example of wave solution to the Maxwell equations in free space
9. (a) [5%] Write down the space-time transformation (Lorentz transformation)
in special relativity for inertial frames with relative velocity v along
the x-axis.
(b) [5%] If two events (t ,x ), (t ,x ) occur at the same space point
1 1 2 2
x = x but at different times t ≠ t , prove that it is impossible to
1 2 1 2
find another inertial frame in which these two events occur
simultaneously under special relativity.
10. For a point particle with mass m and speed v,
(a) [5%] What are the relativistic expressions for its energy and momentum?
(b) [5%] If the speed v is much less than the speed of light c, prove that
the relativistic expressions for energy and momentum approach the
corresponding classical expressions in the Newtonian mechanics.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.66.200
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.217.165.117