課程名稱︰普通物理學甲
課程性質︰系定必修
課程教師︰梁啟德
開課學院：
開課系所︰材料系
考試日期（年月日）︰2009/04/13
考試時限（分鐘）：110
是否需發放獎勵金：是 感謝
（如未明確表示，則不予發放）
試題 :
1.A flat ring of inner radius R1 and outer radius R2 as shown in Fig. 1
carries a uniform surface density σ. Please determine the electric
potential at points along the axis (the X axis).〔10％〕
╴╴╴
╱ ╴ ＼
︱ ／ ╲ ｜
∣∣ ─┼┼───x
｜ ╲╴╱ ｜
╲ ／
￣￣￣
├R2┤
├┤R1
Figure 1
2.A certain X-ray tube operates a current of 6.0 mA and a potential
difference of 80 kV. What is its power in Watt?
3.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.
4.A sphere of radius R0 carries a volume charge density ρe(Fig. 2). A
spherical cavity of radius R0/2 is then scooped out and left empty as shown
in Fig. 2. (a) What is the magnitude and direction of the electric field at
point A?〔10％〕(b) What is the direction and magnitude of the electric
field at point B?〔10％〕
╴╴╴╴╴
╱ ╲
︱ ρe ╴ ｜
B︱ A╱.C╲︱
︱ ╲╴／∣
｜ ｜
╲╴╴╴╴╴╱
(Fig. 2)
5.In the capacitance bridge shown in Fig.3, a voltage V0 is applied and the
variable capacitor C1 is adjusted until there is zero voltage between points
a and b as measured on the voltmeter. Determine the unknown capacitance Cx
if C1 = 8.9μF and the fixed capacitors C2 = 18.0μF and C3 = 6.0μF.
╱｜╲
C1 ╱ ｜ ╲Cx
╴╴╴╴╱ V ╲╴╴╴╴
｜ ╲ ｜ ／ ∣
｜ C2 ╲ ｜ ／C3 ｜
｜ ╲｜／ ∣
︱ ︱
└─ |│───────────┘
V0
Figure 3
6.Two different dielectrics fill the space between the plates of a paraallel-
plate capacitor as shown in Fig. 4. Determine a formula for the capacitance
in terms of the permittivity constant ε0, dielectric constants K1, K2, the
area A, of the plates, and the separation d1 = d2 = d/2. 〔Hint: Can you
consider this capacitor as two in series or in parallel〕〔10%〕
│
────┴──── ─
K1 d1
───────── ─
K2 d2
────┬──── ─
│
Figure 4
7.In the circuit of Fig. 5, ε = 1.2kV, C = 6.5μF, R1 = R2 = R3 = 0.73MΩ.
With C completely uncharged, switch S is suddenly closed (at t = 0). At
t = 0, what are (a) current i1 in resistor 1 [4%]. (b) current i2 in resistor
2,[4%] and (c) current i3 in resistor 3 [4%]? At t approaches infinity, what
are (d) I1 [4%] (e) I2 [4%] and (f) I3 [4%]? what is the potential difference
V2 across the resistor 2 at (g) t = 0 [3%] and (h) t approaches infinity?
[3%]
┌───R1───╱ ──┬───┐
│ S │ │
│ │ R3
│ R2 │
─ │ ＝ C
－ │ │
│ │ │
└───────────┴───┘
Figure 5
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