課程名稱︰普通物理學甲下
課程性質︰系定必修
課程教師︰張顏暉
開課學院：電機資訊學院
開課系所︰電機系
考試日期（年月日）︰2007/04/19
考試時限（分鐘）：160分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Midterm Exam.
1. A hollow cylindrical conductor of length L has inner radius R1 and outer
radius R2. A potential difference is applied between the inner and outer
surfaces so that a current I flows in the outward radial direction. If
σ is the conductivity of the material, what is the resistance of the
cylinder? (10)
2. A cube of side 2a was placed with eight corners located at (±a, ±a, ±a).
Find the electric flux through the box and the total charge inside, if the
electric field is given by (a) E=a i,(b) E=ax i+az k (10)
3. A thin plastic disk of radius R has charge q uniformly distributed over its
surface. If the disk rotates at an angular frequency ω about its axis, what
is the magnetic moment of this spinning disk? (10)
4. An initially uncharged capacitor C is fully charged by a constant emf ε in
series with a resistor R. Show that the final energy stored in the capacitor
is half the supplied by the emf. (10)
5. A soap bubble of radius R0 is slowly given a charge q. Because of mutual
repulsion of the surface charge, the radius increases slightly to R. The air
pressure inside the bubble drops because of the expansion, to P(V0/V) where
P is atmospheric pressure V0 is the initial pressure, express R in terms of
q, ε0, P and R0. (10)
6. The space between two concentric conducting spherical shells of radii a and
b (b>a) is filled with a substance of dielectric constant κ. A potential
difference V exists between the inner and outer shells. Determine (a) the
capacitance of the device and (b) the charge q' induced on the surface of
the dielectrics. (10)
7. Hall effect could be used to determine the carrier concentration and carrier
type in a semiconductor. Describe the arrangement used to measure the Hall
effect. Derive the relation between the Hall voltage and the current that
flows through the sample and find the carrier concentration as a function
of the applied magnetic field. Explain how could the carrier type be
determined in this experiment. (10)
8. Two concentric cylinders of radii a and b (b>a) has a length L. The inner
cylinder has chare Q and the outer cylinder has charge －Q. Treat the
cylinder as infinitely long. Find the energy stored within the two
cylinders. (10)
9. The current density of inside a long solid cylindrical wire of radius a is
in the direction of the axis and varies linearly with radial distance r from
the axis according to J=(J0)r/a. Find the magnetic field inside the wire.
Express the answer in terms of the total current carries by the wire i.
10.A uniform magnetic field fills a cylindrical volume of radius R. If B is
changing at the rate dB/dt. Take the center of the cylinder as the origin.
find the electrical fields (both magnitude and direction) of point A
(-R/4, 0) and B(-R/2,R/4). Find the value of ∫E‧ds around the loop shown
in the figure. The loop has a radius of R/4 and the center of the loop is
at position (-R/2, 0). (10)
_- ─-_
／x x x x＼
/x B x x x x\ (我不太會畫圖...裡面B的位置是loop上的
│x ○A x x x│ 頂端那點，A是loop上最右邊那一點，然後
\x x x x x x/ loop裡面一樣有x的磁場)
＼x x x x／
─
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.240.234
※ 編輯: jasonkuo515 來自: 140.112.240.234 (04/19 20:55)
※ 編輯: jasonkuo515 來自: 140.112.240.234 (04/20 00:01)