課程名稱︰電磁學下 課程性質︰必帶 課程教師︰王立民 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰100/04/26 考試時限（分鐘）：120+10 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 電磁學平時考(Griffiths CH8~CH9.3) 滿分130 Formulas and constants: ε0=8.852*10^-12 (C^2/Nm^2) μ0=4π*10^-7 (N/A^2) h=6.626*10^-34 Js e=1.6*10^-19 C Tzz=0.5ε0(Ez^2-Ex^2-Ey^2)+(0.5/μ0)*(Bz^2-Bx^2-By^2) Tzx=ε0EzEx+(1/μ0)BzBx <r>×<θ>=<ψ> ; <r>×<ψ>=-<θ>; (<θ>)z=-sinθ π ∫ (sinθ)^3 dθ=4/3 0 1.We can use Maxwell stress tensor to calculate the force of magnetic attraction between northern and southern hemispheres of uniformly charged spinning spherical shell (of radius R, carrying a uniform surface charge density σ, spinning at angular velocity ω). It is known that the boundary surface consists of 2 parts -- a hemispherical cap and an equatorial circular disk, where the spinning shell produces an inside magnetic field Bin=(2/3)μ0σRω, and Bout=(μ0m)/(4πr^3)(2cosθ <r> + sinθ <θ>) with a magnetic dipole moment m=(4π/3)σωR^4 <z> (a)Proof (or explain) that the contribution from the outer portion of the xy plane(r>R) can be in place of that from the hemispherical cap.(10%) (b)Use the Maxwell stress tensor to calculate the force as described previously by considering the contributions from the outer portion of the xy plane(r>R) and the equatorial circular disk(r<R).(20%) 2.(a)Consider the same charged spinning spherical shell in Problem 1. Compute the angular momentum stored in the electromagnetic fields.(10%) (b)Suppose we can "ideally" discharge without any momentum loss or gain. Find the "new" angular velocity for the spherical shell of mass M and rotational inertia of rigid body I=(2/3)MR^2.(10%) 3.Picture the electron as a uniformly charged spherical shell as seen in Problem 1. (a)Calculate the angular momentum contained in the fields.(10%) (b)Suppose that the electron's spin angular momentum is entirely due to the field angular momentum in (a): Ltotal=(h bar)/2=h/4π. Determine the speed of a point on the equator and discuss your result. Is it reasonable or not?(10%) (c)We know that Dirac proposed an idea that electric and magnetic charge (a magnetic monopole) must be quantized: (μ0 qe qm)/4π=n*0.5(h bar), for n =1,2,3... Following this idea, calculate the discrete magnetic monopole charge in unit of A．m, where A:ampere.(10%) 4.The intensity of a plane EM wave propagating in vacuum is 1300W/m^2. (a)Find the momentum flux density and energy density of this EM wave.(10%) (b)If this wave strikes a perfect reflector, what pressure does it exert?10% 5.(a)Try to derive the Fresnel's equations for the case of polarization perpendicular to the plane of incidence.(10%) (b)Show that there is no Brewster's angle for any n1 and n2 (index of refrection) with typical case μ1≒μ2.(10%) (c)For peculiar case, n1=1, n2=1.5, μ1=μ0, μ2=2μ0, determine the Brewster's angle.(10%) [Hint: Wave functions: ～ ～ → → EI=E0I exp[i(kI．r -ωt)] <y> ～ ～　　　　→ → BI=(1/v1) E0I exp[i(kI．r -ωt)] (-cosθ1 <x> - sinθ1 <z>) ～ ～ → → ER=E0R exp[i(kR．r -ωt)] <y> ～ ～　　　　→ → BR=(1/v1) E0R exp[i(kR．r -ωt)] (cosθ1 <x> + sinθ1 <z>) ～ ～ → → ET=E0T exp[i(kT．r -ωt)] <y> ～ ～　　 → → BT=(1/v2) E0T exp[i(kT．r -ωt)] (-cosθ2 <x> + sinθ2 <z>) Boundary conditions : (i) ε1*E1(┴)=ε2*E2(┴) (ii) B1(┴)=B2(┴) (iii) E1(∥)=E2(∥) (iv) (1/μ1)B1(∥)=(1/μ2)B2(∥) (┴)表垂直分量；(∥)表平行分量 and use the definitions: α=(cosθ2)/(cosθ1); β=(μ1v1)/(μ2v2). --

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