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）︰96/06/25
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 :
07F Final Exam
1.The current density J inside a long, solid, cylindrical wire of radius a=3.1
mm is in the direction of the central axis, and its magnitude linearly with
radial distance r from the axis according to J = Jo‧r/a, where Jo=310A/m^2.
Find the magnitude of the magnetic field at (a) r=0, (b) r=a/2, (c) r=a. (10%)
2.A thin lens with radius of curvatures (nearer lens surface) R1=42cm and
(farther lens surface) R2=33cm. The index of refraction of the lens n=1.70.
Object O stands in front of the thin lens, on the central axis with object
distance p=35cm. Find (a) the image distance i and (b) the lateral
magnification m of the object, including signs. Also, determine whether the
image is (c) real (R) or virtual (V), (d) inverted (I) from object O or
non-inverted (NI), and (e) on the same side of the lens as the object O or on
the opposite side. (10%)
3.A plane electromagnetic wave, with wavelength 3.0m, travels in vacuum in the
positive direction of an x axis. The electric field, of amplitude 300 V/m,
oscillates parallel to the y axis. What are the (a) frequency, and (b) angular
frequency, and (c) angular wave number of the wave? (d) What is the amplitude
of the magnetic field component? (e) Parallel to which axis does the magnetic
field oscillate? (f) What is the time-averaged rate of energy flow in watts
per square meter associated with the wave? The wave uniformly illuminates a
surface of area 2.0m^2. If the surface totally absorbs the wave, what are (g)
the rate at which momentum is transferred to the surface and (f) the radiation
pressure on the surface? (16%)
4.In an oscillating LC circuit with C=64.0μF, the current is given by
i=(1.60)sin(2500t+0.68), where t is in seconds, i in amperes, and the phase
constant in radians. (a) How soon after t=0 will the current reach its maximum
value? What are (b) the inductance L and (c) the total energy? (10%)
5.A parallel-plate capacitor with circular plates of radius R is being charged
as in Fig.1. (a) Derive an expression for the magnetic field at radius r for
the case r≦R. (b) Evaluate the field magnitude B for R=r/5=11.0mm and
dE/dt=1.50×10^12V/m‧s (c) Derive an expression for the induced magnetic field
for the case r≧R. (10%)
6.In Fig.2, a wire loop of dimensions L=40.0cm and W=25.0cm lies in a
magnetic field B. What are the (a) magnitude ε and (b) direction (clockwise
or counterclockwise - or "none" if ε=0) of the emf induced in the loop if
B=(4.00×10^-2T/m)yk? What are (c) ε and (d) the direction if
B=(6.00×10^-2T/s)tk? What are (e) ε and (h) the direction if
B=(8.00×10^-2T/m‧s)tk? What are (g) ε and (h) the direction if
B=(3.00×10^-2T/m‧s)xtj? What are (i) ε and (j) the direction if
B=(5.00×10^-2T/m‧s)yti? (20%)
7.In Fig.3, a parallel-plate capacitor has square plates of edge length L=
1.0m. A current of 2.0A charges the capacitor, producing a uniform electric
field E between the plates. (a) What is the displacement current Iα through
the region between the plates? (b) What is dE/dt in the region? (c) What is
the displacement current encircled by the square dashed path of the edge
length d=0.50m? (d) What is ∮B‧dS around this dashed path? (12%)
8.Suppose that the two waves in Fig.4 have wavelength λ=500nm in air. What
mulyiple of λ gives their phase difference when they emerge if (a) n1=1.50,
n2=1.60, and L=8.50μm; (b) n1=1.62, n2=1.72, and L=8.50μm; and (c) n1=1.59,
n2=1.79, and L=3.25μm? (d) Suppose that in each of these three situations
the wave arrive ata common point (with the same amplitude) after emerging.
Rank the situations according to the wave produce at the common point. (12%)
Fig.1在普物課本第七版p.864 Fig32-5a
Fig.2:p.819 Fig30-45
Fig.3:p.885 Fig32-33
Fig.4:p.967 Fig35-4
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