課程名稱︰普通物理學甲下
課程性質︰數學系大一必帶
課程教師︰黃暉理
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014/03/11
考試時限（分鐘）：60
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. ~ 3. 圖片：http://i.imgur.com/cOlm6Hb.jpg
1. A plastic rod with charge density λ, is a circular section of radius r and
central angle 2π/3. Point O is the center of the curvature of the rod. A
dipole with charge Q and -Q with distance d is located at O (d<<r). And the
angle between the dipole moment and the plane of the curvarue is θ.(25 pt.)
→
(a) What is the electric field E due to the rod at point O? (15 pt.)
→ →
(b) What is the torque τ on the dipole caused by E ? (5 pt.)
→
(c) What is the potential energy U of the dipole in E ? (5 pt.)
2. Figure shows a section of a conducting rod of radius R = R and length L
1
inside a thin-walled coaxial conducting cylindrical shell of radius R = 10R
2
and the (same) length L. The net charge on the rod is Q = Q; that on the
1
shell is Q = -2Q. What are the (a) magnitude E and (b) direction (radially
2
inward or outward) of the electric field at radial distance r = 2R ? What
2
are (c) magnitude E and (d) the direction at r = 5R ? What is the charge on
1
the (e) interior and (f) exterior surface of the shell? (Show your answer by
Q and R) (10 pt. for (a)(b) and (c)(d), 5 pt. for others)
3. (a) Figure (a) shows a nonconducting rod of length L and uniform linear
charge density λ. Assume that the electric potential is defined to be V = 0
at infinity. What is V at point P at distance d along the rod's
perpendicular bisector? (15 pt.) (b) Figure (b) shows an identical rod
except that one half is now negatively charged. With V = 0 at infinity, what
is V at P? (10 pt.)
4. Figure shows a parallel-plate capacitor of plate area A and plate separation
d. A potential difference V is applied between the plates by connecting a
0
battery between them. The battery is then disconnected, and a dielectric
slab of thickness b and dielectric constant κ is placed between the plates
as shown.
(a) What is the capacitance C before the dielectric slab is inserted?
0
(b) What is the electric field E in the gaps between the plates and the
0
dielectric slab?
(c) What is the electric field E in the dielectric slab?
1
(d) What is the potential difference V between the plates after the slab has
been introduced?
(e) What is the capaitance with the slab in place between the plates of the
capacitor?
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