[試題] 98下 電機系 電磁學 期中考
課程名稱︰電磁學
課程性質︰電機系必修
課程教師︰江衍偉
開課學院：電機資訊學院
開課系所︰電機系
考試日期（年月日）︰99.4.23
考試時限（分鐘）：100
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(以下以黃色字體表示單位向量,亮字表示向量)
1.(6%) Consider two points P(r,θ,ψ) and Q(r+dr,θ+dθ,ψ+dψ) at
differential distance in the spherical coordinate system. Please write the
expressions for three side lengths that would define the differential volume
formed by incrementing the coordinates from point P to point Q.
2.(8%) For the current element Idx(ax+ay)(A-m) situated at the point (1,-2,2),
find the magnetic flux density at the point (2,-1,3).
3.(8%) Prove that for any vector field A the vloume integral
∫ (▽‧▽ X A )dv = 0
v
Please state clearly the theorems you use.
4.(8%) At time t=0 a rigid straight line section of metallic wire of length
L(m) is situated on the y-axis with its tips located at (0,L/2,0) and
(0,-L/2,0), respectively, and in the whole free space there exists a
uniform magnetic field, B = √3B0ax + B0az (Wb/m^2) , where Bo is a positive
constant. Now the line section is moved with constant velocity, v(m/s),
along the z-direction. What is the open-circuit voltage induced between the
tips of the line section? Also explain which tip has higher potential.
5.(15%) Find the unit vector normal to the surface 2x^2+y^2=6 at the point
(√2,√2,0).
6.(20%) A circular ring of radius a lies in the xy-plane and has its center at
the origin. The ring is coated with charge such that the charge density is
given by ρL=ρL0 sinψ(C/m), where ψ is the angle variable as in the
cylindrical or polar coordinate system. Find the electric field intensity
vector at a point on the z-axis.
7.(20%) For the electric field E = E0^(-kx)cos((3*10^8)t-y)az in free space
(J=0), find the value(s) of k for which the field satisfies both of
Maxwell's curl equations.
8.(15%) Current I flows along a straight wire from a point charge Q1(t)
located at (1,1,2) to a point charge Q2(t) located at (0,0,1). Find the line
integral of the magnetic field intensity vector H along the square closed
path having the vertices at (1,1,0), (-1,1,0), (-1,-1,0), and (1,-1,0) and
traversed in that order.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.7.59
※ 編輯: f28525 來自: 140.112.7.59 (04/23 16:20)
推
04/23 19:46, , 1F
04/23 19:46, 1F
※ 編輯: f28525 來自: 114.45.56.42 (04/24 11:59)
推
04/25 00:32, , 2F
04/25 00:32, 2F