課程名稱︰普通物理學甲下
課程性質︰大一必修
課程教師︰梁啟德
開課系所︰生機系
考試時間︰94.4.20
試題 :
1.A parallel-plate capacitor whose eapacitance C is 13.5pF (1pF=1*10^-12 Farad)
is charged to a potential difference Ｖ=12.5V between its plates.The charging
battery is now disconnected and porcelain slab (dielectric constant κ=6.50)
is slipped between the plates.What is the electric potential energy of the
device,both before (10%) and after (10%) the slab is introduced?
ε0=8.85*10^-12 (C^2/N*m^2)
2.A rod lies parallel to the x axis of inertial reference frame S,moving along
this axis at a speed of 0.630c where c is the speed of light in vacuum.Its
rest length is 1.70m.What will be its measured length is frame S?(10%)
[Hint:Length contraction]
3.Please calculate the electric field E(z) (10%) and the electric potential
V(z) (10%) at points at the center axis of a plastic disk of radius R that
has a uniform charge density of one surface.Here z corresponds to the
distance between any point at the center axis of the disk and the center of
the disk.The surface charge density of the disk is given by σ (in units of
C/m^2).
4.A certain X-ray tube operate a current of 7.0mA and a potential difference
of 80kV.What is its power in Watt?(10%)
5.Please prove the following statement.If an excess charge is placed on an
isolated conductor,that amount of charge will move entirely to the surface
of the conductor.None of the excess charge will be found within the body of
the conductor.(10%)
6.RC circuit.Figure 1 shows that when switch S is closed on a,the capacitor is
charged through the resistor.Please show that the charge on the capacitor
q(t) is given by q=Cξ(1-e^(-t/RC)) where t is time (10%)[Hint:q(t=0)=0]
┌────a
│
│ ────^^^^^────┐
│ R │
│ b │
│ │ │
+│ │ │
─ │ ─
ξ – │ C ─
-│ │ │
│ │ │
│ │ │
└───┴──────────┘
Figure 1
7.Free expansion.When n moles of an ideal gas double its volume in a free
expansion,the entropy increase from the initial state to the final state f
is given by Sf-Si=nR㏑2 Where R is the gas constant.Please use the
Boltzmann's entropy equation S=k㏑W and Stirling's approximation
㏑N!=N(㏑N)-N when N (the number of ideal gas molecules) is large to prove
that Sf-Si=nR㏑2.[Hint:k=nR/N is the Boltzmann constant and W is the number
of microstates](10%)
8.A conducting sphere of radius 10cm has an unknown charge.If the electric
field 15cm from the center of the sphere has the magnitude 3.0*10^3 N/C and
is directed radially inward,what is the net charge of the sphere?(10%)
ε0=8.85*10^-12 (C^2/N*m^2)
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