課程名稱︰普通物理學
課程性質︰
課程教師︰林敏聰
開課系所︰電機系
考試時間︰2005/4/26
試題 :
1.Please write down the (four) Maxwell's equations (6%) and give a brief inter
-pretation for each one.(4%)
2.It is well known that the capacitance of two parallel metallic plates is
given by Co=εo*A/d, whereεo, A , and d are dielectric constant, area of
the plate, and the separation between the plates respectively. In the deri-
vation of the formula, it is assumed that the charges are accumulated only
at the surface of the plate, which is not necessarily true mesoscopically.
If the charges are uniformly distirbuted over a thin thickness δ,instead of
the surface only, show that the capacitance, C' is given by 1/C'=1/Co+1/Ci,
with Ci=εo*A/δ (15%)
3.Total charges Q are uniformly distributed inside a rigid nonconducting sphere
with mass m, radius R, which is spinning about its symmetry axis along z
direction with angular velocity ω. Now a magnetic field B is applied along x
axis.Show that the sphere will precess along x axis and derive its precession
frequency.(10%)
4.A magnetic damping system utilizes induction current which will generate
force if placed in a magnetic field. Let's see how it works. If large metal
plate with conductivity σ and thickness t is moving with velocity v through
an area, A, inside which passes magnetic flux density B, uniformly. Show that
there will be a force pulling back the plate, and derive its magnitude.(10%)
5.Please derive the number density n of charge carriers with charge e in con-
ducting strip of thickness l carrying a current I placed in a magnetic field
B, creating a potential difference V across the strip (Hall effect).(15%)
6.Please describe what is the fundamental interaction (force) involved in the
frictional force.(10%)
7.A parallel-plate capacitor has square plates 1.0 m on a side as shown in the
figure below. Acurrent of 2.0 A charges the capacitor, producing a uniform
electric field E (vector) between the plates, with E (vector) perpendicular
to the plates. (a) What is the displacement current Id through the region
between the plates?(5%) (b)What is dE/dt in the region?(5%) (c)What is the
displacement current through the square dashed path between the plates?(5%)
(d) What is ∮B˙ds (B,s both vectors and make dot operation) around this
square dashed path?(5%)
│↓i ┌───┐┬
─┴─ │ ← │
─┬─ │ ↓ ↑│1.0m the path is a square 0.5m*0.5m
│↓i │ → │
└───┘┴
Edge view Top view
8.The long-range magnetic ordering, such as ferromagnetism and antiferromagnet-
ism, is often attributed to an exchange coupling or exchange force.Is the
exchange force. Is the exchange force really a fundamental interaction? If
not, what is its physical origin?(10%)
Good luck!!!(Total 100%)
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