課程名稱︰古典電力學上
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）︰10/12/10
考試時限（分鐘）：120min
是否需發放獎勵金：Yes
（如未明確表示，則不予發放）
試題 :
1 Answer “yes” or “no” to the following statements (no explanation is
is required ) Notations follow Jackson . Two point for each correct answer ;
no penalty for wrong answers .(24%)
(1) Eq (1.13) gives exactly the same information as Eq (1.15)
(2) ε_0 E^2 (x)and qδ(x-x_0)φ(x) have the same dimension
(3) Legendre function of the first kind P_ν (x)diverges at x=1 unless ν an
integer .
(4) Bessel function of the first kind J_n (x) is a monotonically increasing
function of x , where n is a positive integer .
(5) Electric polarization and electric dipole moment do not have the same
dimension
(6) The polarization charge density (ρ_pol=-▽˙P)is only a convenient
definition It does not represent real charges .
(7) φ(x) in (4.84) does not include contribution from the polarization charge
(8) Eq(4.89) can be applied to a linear , anisotropic , and nonuniform
dielectric medium .
(9) In magnetostatics , ∫_νJd^3x=0for an arbitrary volume (ν) of integration
(10) Eq(5.22) gives exactly the same information as Eq(5.24)
(11) Eq(5.147) is derived from Eq(5.146) under the assumption that the volume
of integration is infinity .
(12) A static magnetic field can penetrate through a conductor with
μ=μ_0 as if there were no conductor present .
2 A point charge q is brought from infinity to a distance d from an infinite
grounded , plane conductor . If the induced surface charge on the conductor is
now "frozen" in place and the point charge is removed , what is the energy in
the remaining electric field ?(15%)
3 A conducting sphere of radius a with net charge Q on its surface is placed in
a uniform electric field E_0 (e_z ) ? . Use the method of expansion to find φ
outside the sphere .
4 (a) Refer to the mechanism of dipole formation discussed in Sec4.6 . Find the
energy required to induce a dipole on an atomic or molecular charge e by an
electric field E ? .(8%)
(b) From W=1/2 ∫E。D d^3x [(4.89)] , we deduce that , in a dielectric
, the energy density due to the presence of E ? is w=1/2 E ??D ? . Derive this
relation using the result in part (a) .(8%)
5 Explain why the derivation of the magnetic field energy in Jackson Sec 5.16
is valid only when the current J ? is established at an infinistesimally small
rate. (10%)
6 A copper rod of length L is pivoted at one end and rotates with constant
angular velocity ω about an axis perpendicular to its length . A uniform
magnetic induction B ? is applied parallel to the axis of rotation .
Calculate the potential difference between the ends of the rod ? (15%)
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