課程名稱︰普通物理學甲下
課程性質︰必修
課程教師︰王建萬
開課學院：工學院
開課系所︰工科海洋學系
考試日期（年月日）︰99/4/23
考試時限（分鐘）：110
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
10S Mid Term Exam
1. In Fig.1, a solid sphere of radius a=6.00cm is concentric with a spherical
conducting shell of inner radius b=2.00a and outer radius of c=3.00a. The
sphere has a net uniform charge q1=+6.00fC; the shell has a net charge
q2=-q1. What is the magnitude of the electric field at radial distances
(a) r=0, (b)r=a/2.50, (c) r=a, (d) r=1.80a, (e) r=3.00a, and (f) r=6.00a?
What is the net charge on the (g) inner and (h) outer surface of the shell?
(16%)
2. In Fig.2, R1 =8.00Ω, R2 =16.0Ω, R3=6.00Ω, and the ideal battery's emf is
ξ=48.0 V.For what value of R4 will the rate at which the battery transfers
energy to the resistors equal (a)100.0W, (b) the maximum possible rate Pmax,
and (c) the minimum possible rate Pmin? What are (d)Pmax and (e)Pmin?
(10%)
——— R1 ———————————
∣ ∣ ／∣
∣ ∣ ∣
∣ ∣ R4 ∣
——
-- ξ R2 ／ R3
∣ ／
∣ ∣ ／ ∣
∣ ∣／ ∣
———————————————— Fig.2
3. Fig.3 shows a parallel-plate capacitor of plate area A and a separation d.
A potential difference Vo is applied between the plates.The battery is then
disconnected, and a dielectric slab of thickness b and dielectric constant
k is placed between the plates as shown. Assume A = 140cm^2, d = 1.20cm,
Vo = 92.0V, b = 0.720cm, and k = 2.80. (a) What is the capacitance Co before
the dielectric slab is inserted? (b) What free charge appears on the plates?
(c) What is the electric field Eo in the gaps between the plates and the
dielectric slab? (d) What is the electric field E1 in the dielectric slab?
(e) What is the potential difference V between the paltes after the slab
has been introduced? (f) What is the capacitance with the slab in place
between the plates of the capacitor? (12%)
————————
+q ∣+ + + + + + + ∣ —
———————— ↑
∣
—————————— —∣
-q' ∣ ¯¯¯¯¯¯¯¯k∣ ↑∣
∣ + + + + + + + + ∣ b d
+q' —————————— —∣
∣
———————— ↓
-q ∣¯¯¯¯¯¯¯∣ — Fig.3
————————
4. Fig.4 is a section of a contucting rod of radius R1 = 2.00mm and length
L =16.00m inside a thin-walled coaxial conducting cylindrical shell of
radius R2 = 6.00R1 and the same length L. The net charge on the rod is
Q1=+6.00x10^-12C; that on the shell is Q2=-3.00 Q1.What are the(a) magnitude
E and (b) direction (radially inward or outward) of the electric field at
radial distance r = 2.00R2? What are (c) E and (d) direction at r = 3.00R1?
What is the charge on the(e) interior and (f) exterior surface of the shell?
(12%)
5. In Fig.5, a potential difference V =160V is applied across a capacitor
arrangement with capacitances C1 =12.0μF, C2 =8.00μF, and C3 =6.00μF.
What are (a) charge q3, (b) potential difference V3, and (c) stored energy
U3 for capacitor 3, (d) q1, (e) V1, and (f) U1 for capacitor 1, and (g) q2,
(h) V2, and (i) U2 for capaciotr 2? (16%)
———————∣∣——
↑ ∣ ∣
∣ ∣ C2 ∣
— ∣
V C1 — ∣
∣ ∣
∣ C3 ∣ ∣
↓ ∣ ∣
—∣∣———————— Fig.5
6. A 8.00g block with a charge of +12.0×10^(-6)C is placed in an electric
field E=(4000i-800j) N/C. What are the (a) magnitude and (b) direction
(relative to the positive direction of the x axis) of the electrostatic
force on the block? If the block is released from rest at the origin at
time t=0,what are its (c) x and (d) y coordinates at t = 5.00 s? (9%)
7. Two isolated, concentric, conducting spherical shells have radii R1= 0.400m
and R2=1.20m, uniform charges q1=+3.00μC and q2=+1.20μC, and negligible
thickness.What is the magnitude of the electric field E at radial distance
(a) r=4.00m, (b) r=0.600m, and (c) r=0.300m? With V=0 at infinity, what is V
at (d) r=4.00m, (e) r=1.20m, (f) r=0.800m, (g) r=0.400m, (h) r=0.200m, and
(i)r=0? [1/(4πεo) = 8.99x10^9 N.m^2/C^2] (16%)
8. An electron follows a helical path in a uniform magnetic field given by
B = (30i-40j-60k)mT. At time t = 0, the electron's velocity is given by
v = (40i+20j-60k)m/s. (a) What is the angel ψ between v and B? The
electron's velocity changes with time. Do (b) its speed and(c)the angel ψ
change with time? (d) What is the radius of the helical path? (9%)
[electron mass m=9.11x10^-31kg, electron charge q=-e=-1.60x10^-19C]
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