課程名稱︰普通物理學甲
課程性質︰
課程教師︰梁啟德
開課系所︰材料系
考試時間︰2 hr
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
Final examination (21/6/2006)
1. Please write down Maxwell;s equations. [Hint: There are four of them
in total.] (20%)
2.A nonconducting sphere has mass 80.0g and radius 20.0 cm. A flat
compact coil of wire with 5 turns is wrapped tightly aroundit, with each
turn concentric with the sphere. As shown in Fig.1, the sphere is placed
on an inclined plane that slopes downward to the left, making an angleθ
with the horizontal, so that the coil is parrallel the the inclined plane.
A uniform magnetic field of 0.350 T vertically upward exists in the region
fo the spere. What current in the coil will enable the sphere to rest in
equilibrium on the inclined plane? (10 %)
Fig.1 一斜面上有一球，斜面角度θ，球上有線圈平行斜面，磁場B垂直向上。
3. The voltage source in Fig2 has an output of ΔVrms= 100 V at ω =
1,000 rad/s. Determine (a) the current(rms) in the circuit and (10%)
(b) the power supplied by the source. (10%) (c) Show that the power
delivered to theresistor is equal to the power supplied by the source.
(10%)
Fig.2 一迴路，順時鐘依序為交流電電源，50.0μF電容，40.0Ω電阻，50.0mH電感。
4. A beam of 580-nm light passes throught two closely space glass plates,
as shown if Fig.3. For what minimum onozero value of the plate separation
d is the transmitted light btight? (10%)
Fig.3 二玻璃板，光穿越第一片，在第二片一分為二，一直接穿過，一反射碰到第
一片，再反射，穿越第二片。
5. Michael Jordan is 198 cm tall. How tall must a vertical mirror be if
he is to be able to see his entire length in it? (10%)
6.(a) Light traveling in a medium of refractive index n1 is incident at
an angleθ on the surface of a medium of index n2. The angle between
reflected and refracted rays isβ. Show that (10%)
tanθ= n2*sinβ/(n1-n2*cosβ)
(Syggestion: Use the identity sin(A+B) = sinAcosB + cosAsinB.) (b) Show
that this expression for tanθ reduces to Brewster's law when β=90°,
n1=1, nad n2=n
The permittivity ε0=8.85*10^-12 C^2/Nm^2
The permeability constant μ0=4π*10^-7 Tm/A
4.
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