[試題] 99下 林敏聰 普物甲下 期中考
課程名稱︰普物甲下
課程性質︰
課程教師︰林敏聰
開課學院：
開課系所︰
考試日期（年月日）︰100.4.20
考試時限（分鐘）：160min
是否需發放獎勵金：Yes
（如未明確表示，則不予發放）
試題 :
1. (a)What are the two basic postulates in special relativity?(5%)
(b)Please derive the results of time dilation and length contraction in
an inertial reference moving with a constant velocity V in the
x-direction with respect to the inertial frame at rest.(10%)
(c)Please write down and derive the coefficients of the Lorentz
transformation.(10%)
2. (a)Please write down the definition of potential V from a potential
difference (Vf - Vi) and differential work done on the charge.(5%)
(b)Please show that V due to a point charge q can be expressed as
V = q/(4πεr) (10%)
3. Consider an arbitary charge distribution p(r) with a volume V. Please
express the electric potential q(r) with terms of monopole charge, dipole
moment, and quadrupole moment. (Hints: using binomial expansion).(15%)
4. Two electrons are fixed 2.0cm apart. Another electron is shot from infinity
and stops midway between the two. What is its initial speed? (10%)
5. Two identical conducting spheres, fixed in place, attract each other with
an elextrostatic force of 0.108N when their center-to-center separation is
50.0cm. The spheres are then connected by a thin conducting wire. When
the wire is removed, the spheres repel each other with an electrostatic
force of 0.0360N. Of the initial charges in the spheres, what was (a) the
negative charge on one of them and (b) the positive charge on the other?
(20%)
6. Two space ships are traveling in the opposite directions. Space ship 1 with
(v1, L1) is approaching space ship 2 with (v2, L2), where vi is the velocity
measured by a observer at rest and Li is the rest length of the space
ship i.
(a) How long is the time, measured by the observer at rest, for the two
space ships being next to each other? (5%)
(b) How long is the time, measured by the person in space ship 1, for the
two space ships being next to each other? (5%)
(c) Please transform the time you get in (b) to the rest frame. Do you get
the same answer in (a)? Explain your result. (5%)
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