課程名稱︰普通物理學甲下
課程性質︰必修
課程教師︰陸駿逸
開課學院：理學院
開課系所︰化學、地質
考試日期（年月日）︰2015.6.23
考試時限（分鐘）：120
試題 :
1.Write down the four Maxwell equations. Describe two experiments which are
related to these equations. Point out the connection between the experiments
and equations.
2.A solenoid with length 20cm, 300 turns and cross-section 10cm^2 is carrying
a current 2.0A.
(a)What is the energy density inside the solenoid?
(b)What is the stored magnetic energy?
3.A RLC circuit with R=5.0Ω, C=20μF, L=2.0H.
(a)Suppose at t=0 the capacitor is partially charged with q(t=0)=5.0E-5(C),
i(t=0)=1.0E-2 (A). Calculate the oscillating frequency with resister into
account.
(b)Calculate the charge q(t).
(c)If the circuit is driven by an emf with the angular frequency
ω=500(sec^-1), calculate the impedance Z of the circuit.
4.Consider the classical model of a hydrogen atom, where the electron, with
mass=m and charge=(-e), is moving in a circular orbit around the nucleus.
Consider the electron motion as a steady circular current, show that the
orbital angular momentum of the electron is proportional to the magnetic
dipole moment Lαμ, and obtain the proportional constant.
5.Write the Biot-Savart law. Comment on its relation between the Ampere's law.
6.An EM wave travels from air toward an ice. Suppose that the air correspond
to z<0 and the ice region is z>0. The refractive index of air is 1.0 and the
ice is 1.3 for the EM wave.
The incident wave is described by
→ ^ → ^
Ei=y E0ie^(i(ki˙r-ωt))
→ ^ ^ → ^
Bi=ki╳y (E0i/c)e^(i(ki˙r-ωt))
→ ^
where ki=(ki)(sina,0,cosa) ki=(sina,0,cosa)
The reflected wave
→ ^ → ^
Er=y E0re^(i(kr˙r-ωt))
→ ^ ^ → ^
Br=kr╳y(E0r/c)e^(i(kr˙r-ωt))
→ ^
where kr=(kr)(sina,0,-cosa) kr=(sina,0,-cosa)
The transmitted wave
→ ^ → ^
Et=y E0te^(i(kt˙r-ωt))
→ ^ ^ → ^
Bt=kt╳y(E0t/c)e^(i(kt˙r-ωt))
→ ^
where kt=(kt)(sinb,0,cosb) kt=(sinb,0,-cosb)
and c/n=ω/kt is the light speed in ice.Recall that
1.0sina=1.3sinb(Snare's law)
(a)Consider a thin volume across the z=0 surface. Show that the Gauss law of
magnetic field implies E0i+E0r=E0t
(b)Consider a small loop across the z=0 surface in the x-z orientation with
vanishing area. Show that the Ampere-Maxwall law implies
kicosa(E0i-E0r)=ktcosbE0t
(c)For a given incident angle a=π/6, solve the ratios of E0r/E0i and E0t/E0i.