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這是 18.Apr.2003的考題 連載第三份囉!!!
考題來源: Steggie (大家謝謝她吧^^)
然後按照之前她打考古題的慣例...我打的時候把沒出現過的題目標黃色
1. Please write down the (four) Maxwell's equations (6%)
and give a brief interpretation for each one. (4%)
2. In Fig 1, two identical, electrically isolated conducting spheres A and B
are separated by a (center-to-center) distance a that is large compared to
the spheres. Sphere A has positive charge of +Q, and sphere B is
electrically neutral. Initially, there is no electrostatic force between
the spheres. (Assume that there is no induced charge on the spheres
because of their large separation.)
(a) Suppose the spheres are connected for a moment by a conducting wire.
The wire is thin enough so that any net charge on it is negligible.
What is the electrostatic force between the spheres after the wire is
removed? (10%)
(b) Next, suppose sphere A is grounded momentarily, and then the ground
connection is removed. What now is the electrostatic force between
the spheres? (10%)
● q=0
B
(兩球心距離a)
Fig.1
● +Q
A
3. A large, flat, nonconducting surface has a uniform charge density σ.
A small circular hole of radius R has been cut in the middle of the
surface, as shown in Fig. 2. Ignore fringing of the field lines around
all edges, and calculate the electric field at point P, a distance z from
the center of the hole along its axis. (Hint: Use superposition) (10%)
Fig.2 : 有一個平面 上面畫滿 +
有一條線 從高處P點 連到平面 並垂直於此平面 (此線應該就是axis)
以此線與平面交點為圓心 半徑R 於此平面上畫一個圓 把他挖空
(就是整個平面上 只有這一塊沒有+符號)
4. What is the capacitance of plate area A, shown in Fig.3?
Fig.3 : 有一個長方形 寬是 2d 長沒給 可是面積是 A
先從長邊把它切一半 其中一半裡面寫著K1
另外一半 再從寬邊把它切一半 這兩半分別寫著K2, K3
5. A parellel-plate capacitor has square plates 1.0m on a side as shown in
Fig. 4. A current of 2.0A charges the capacitor, producing a uniform
electric field 向量E between the plates, with 向量E perpendicular to the
plates.
(a) What is the displacement current Id (d是下標) through the region
between the plates? (5%)
(b) What is dE/dt in this region? (5%)
(c) What is the displacement current through the square dashed path
between the plates? (5%)
(d) What is closed積分符號 向量B d向量s around this square dashed path?
(5%) (就是∮B ds)
Fig.4 : 0.50m
│ ├─←┤
i↓│ ↓ │ 1.0m
══┼══ │ ↑
i↓│ └→─┘
│
Edge View Top View
(好像圖上還有一點點東西 可是實在看不清楚那印刷了|||)
6. Please give the definitions of electric and magnetic dipole ρ and μ. (5%)
What is their torque and potential energy in electric and magnetic
field. (5%)
7. Please derive the orbital magnetic dipole moment μarb of an electron in
an atom with its orbital angular moment Larb (10%)
(μarb, Larb: arb是下標)
8. Please derive the number density n of charge carriers with charge e in
conducting strip of thickness L carrying a current I placed in a magnetic
field B, creating a potential difference V across the strip.
(Hall Effect) (10%)
9. Good Luck! (Total 100%)
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歡迎轉錄^^
這次是怎樣 題目都有一堆圖||| 已經很努力描述了XD
大家看不懂我再描述什麼的話 請推文告知一下XD
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錯誤訂正: 2002年那一份的第三題配分是15分 orz
大家自行注意一下吧 sorry
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