[試題]

[it5606 (海賊˙火影KUSO )]

課程名稱︰普通物理學(甲)
課程性質︰必修
課程教師︰梁啟德
開課系所︰生機系
考試時間︰94.6.22

試題 :
1. Heiseisenberg's uncertainty principle tells us that △Px△X>=h/(2π)

   where△Px and△X  represent the intrinsic uncertainties in the

   measurements of the x component of r and P and h is the Planck constant

   Please prove that in a one-dimension system,Eq.1  is equivalent to

   △E△t>=h/(2π) where △E  and △t represent the intrinsic uncertainties

   in the measurements of the energy and time,respectively(10%)[Hint:Consider

   the kinetic energy of the particle △E]


2.Please write down Maxwell's equations[Hint:There are four of them in total]

3.We wish to use a glass plate with index of refraction n=1.57 to polarize

  light in air (a)At what angle of incidence is the light reflected by the

  glass fully polarized?(10%)(b)What is the corresponding angle of refraction?

  (10%) [Hint:Brewster's angle and polarization by reflection]


4.a capacitor in an LC oscillator has a maximum potential difference of 17V

  and a maximum energy of 160μJ. When the capacitor has a potential

  difference of 5V and an energy of 10μJ,what are (a)the emf across the

  inductor (10%)and (b)the energy stored in the magnetic field(10%)?


5.a charge q is distributed uniformly around a thin ring of radius r. The

  ring is rotating about an axis through its center and perpendicular to

  its plane,at an angular speed ω. Please show that the magnetic moment

  due to the rotating charge is μ=qω(r^2)/2(10%)

6.米高˙佐敦高198cm 一個直立的鏡子可以使他看見整個身高,則此鏡至少多高?


7.Quantum Hall effect.Let us start with the classical Hall effect(a)Please

  prove that in a two-dimension(2D) electron system,the Hall resistance is

  given by R=V/I=B/ne  where V is the Hall potential difference,I is the

  current,B is the applied perpendicular magnetic field,n is the carrier

  concentration(in cm^(-2)) and e is the electron charge,respectively.(5%)

  It has been shown that at extremely low temperatures and high magnetic

  field,the Hall resistance R shows quantized values.From simple calculations

  we know νeB/h=n where ν is the Landau level filling factor,h is the Planck

  constant and n is the carrier density. Please prove R=h/(e^2)ν(5%) This is

  the Nobel-prize wining integer quantum Hall effect [Hint:In 2D,the current

  density is given by J=I/w  where w is the width of the 2D system. Ohm's law

  is given byE=ρJ where ρ=R is the Hall resistivity in 2D.]

看起來題目很難

其實都很簡單

尤其最後一題只是公式代換而已

看了鏡子那題應該就知道老師大放送了




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