課程名稱︰普通物理學甲下
課程性質︰共同必修
課程教師︰王建萬
開課學院：
開課系所︰生工系
考試日期（年月日）︰96/04/23
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 :
07S Mid Term Exam
1.Imagine a Carnot engine that operates between the temperatures Th=850K and
Tl =300K. The engine performs 1200J of work each cycle, which takes 0.25s. (a)
What is the efficiency of this engine? (b) What is the average power of this
engine? (c) How much energy │Qh│ is extracted as heat from the high-
temperature reservoir every cycle? (d) How much energy │Ql│ is delivered as
heat to the low-temperature reservoir every cycle? (e) By how much does the
entropy of the working substance change as a result of the energy transferred
to it from the high-temperarure reservoir? From it to the low-temperature
reservoir? (10%)
2.A 10.0g block with a charge of +8.00×10^(-5)C is placed in an electric
field E=(3000i-600j) 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=3.00s? (10%)
3.Two isolated, concentric, conducting spherical shells have radii R1=0.500m
and R2=1.00m, uniform charges q1=+2.00μC and q2=+1.00μC, and negligible
thicknesses. What is the magnitude of the electric field E at radial distance
(a) r=4.00m, (b) r=0.700m, and (c) r=0.200m? With V=0 at infinity, what is V
at (d) r=4.00m, (e) r=1.00m, (f) r=0.700m, (g) r=0.500m, (h) r=0.200m, and (i)
r=0? (16%)
4.A parallel-plate capacitor has plates of area 0.12m^2 and a seperation of
1.2cm. A battery charges the plates to a potential difference of 120V and is
then disconnected. A dielectric slab of thickness 4.0mm and dielectric
constant 4.8 is then placed symmetrically between the plates. (a) What is the
capacitance before the slab is inserted? (b) What is the capacitance with the
slab in place? What is the free charge q (c) before and (d) after the slab is
inserted? What is the magnitude of the electric field (e) in the place between
the plates and dielectric and (f) in the dielectric itself? (g) With the slab
in the place, what is the potential difference across the plates? (h) How much
external work involved in inserting the slab? (16%)
5.What is the current in a wire of radius R=3.40mm if the magnitude of the
current density is given by (a) Ja=Jo r/R and (b) Jb=Jo(1-r/R), in which r is
the radial distance and Jo=5.50×10^4 A/m^2? (c) Which function maximizes the
current density near the wire's surface? (10%)
6.A neutral water molecule (H2O) in its vapor state has an electric dipole
moment of magnitude 6.2×10^(-30) C.m. (a) How far apart are the molecule's
centers of positive and negative charge? (b) If the molecule is placed in an
electric field of 1.5×10^4 N/C, what maximum torque can the field exert on
it? (c) How much work must an external agent do to rotate this molecule by
180° in this field, starting from its fully aligned position, for which θ=0?
(10%)
7.In Fig.1, a solid sphere of radius a=2.00cm is concentric with a spherical
conducting shell of inner radius b=2.00a and outer radius of c=2.40a. The
sphere has a net uniform charge q1=+5.00fC; the shell has a net charge q2=-q1.
What is the magnitude of the electric fieldat radial distances (a) r=0, (b)
r=a/2.00, (c) r=a, (d) r=1.50a, (e) r=2.30a, and (f) r=3.50a? What is the net
charge on the (g) inner and (h) outer surface of the shell? (16%)
8.In Fig.2, the resistances are R1=1.0Ω and R2=2.0Ω, and the ideal batteries
have emfs ε1=2.0V and ε2=ε3=4.0V. What are the (a) size and (b) direction
(up or down) of the current in battery 1,the (c) size and (d) direction of the
current in battery 2, and the (e) size and (f) direction of the current in
battery 3? (g) What is the potential difference Va-Vb? (12%)
k=8.99×10^9 N·m^2/C^2
εo=8.85×10^-12 C^2/N·m^2
Fig1在普通物理課本第七版中文版p625 Fig.23-50
Fig2:p727 Fig.27-40
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