課程名稱︰古典電力學
課程性質︰必修
課程教師︰朱國瑞
開課學院：理學院
開課系所︰物理所
考試日期（年月日）︰100.01.14
考試時限（分鐘）：102MIN
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1 An ideal dipole p=(3(e_x )+4(e_y ))coulomb-meter is located at the origin in
free space . Find the force (in vector form) it exerts on an electron located
at x=((4e_x)+3(e_y)) meters . [e=1.6×?10?^(-19)Coulomb . The permittivity of
free space (ε_0)is given in Jackson , p.782](10%)
2 Consider two point charges q_1 and q_2 with velocity (ｖ_1 )=v_1 (e_y ) and
(ｖ_2 ) =v_2 (e_z ) respectively Consider two point charges q_1 and q_2
with velocities (ｖ_1 ) =v_1 e_y and (ｖ_2 )=v_2 e_y , Respectively .
If v_1 and v_2<<c (as is assume here) , the electric and magnetic field due
to q1 and q2 can be approximated by the static laws[i.e.Eqs(5.14)and(5.15)
in Jackson].
(a) Calculate the force on q_(1 )due to q_(2 ) and the force on q_(2 )due to
q_(1 )when q_(2 )is a distance of d in front of q_(1 )(10%)
(b) Are the forces on the two charges equal in magnitude and opposite in
directions as required by Newton's third law? Explain your answer in terms
of the conservation of linear momentum(10%))
3 A conducting surface has a static surface change density σ . Use the
Maxwell stress tensor [Jackson Eqs(6.120) and (6.122)] to show that the force
per unit area on the conducting surface is σ^2/2ε_0. (15%)
4 Using Jackson Eqs. (7.4) , (7.56) and (7.58) and assumeing ω<<γ_0,
derive the skin depth (δ) of a good conductor . (16%)
5 Refer to the generalized dielectric constant ε in Jackson Eq (7.51) or
(7.56) . Answer the following questions briefly and to the point .
(a) What are the approximations made on the electron binding force and
in the calculation which result in the linear property of the medium?(8%)
(b) What makes the medium dispersive?(4%)
(c) What makes the medium lossy?(5%)
(d) In the DC limit (ω→0), we have ε→∞ due to the free electrons.
Hence, the derivation is no longer valid . What is the physical reason for the
breakdown?(5%)
6 (a) Calculate the peak electric field (E_0) associate with a linear
polarized laser beam (In free space) having a time-averaged energy density of
10^6 joules/cm^3 .(10%)
(b)What is the peak magnetic induction (B_0) of this laser beam?(10%)
貼完了
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