課程名稱︰電磁學上
課程性質︰系必修
課程教師︰陳正弦
開課學院：理學院
開課系所︰物理學系
考試日期（年月日）︰2008/11/06
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. (10 pts.)
An thin infinite plane carries a uniform surface charge density σ. Find its
electric field (a) by using Gauss's law and (b) by direct integration from
the Coulomb's law which relates electric field to charge density.
2. (10 pts.)
Find the potential inside and outside a uniformly charged solid aphere with
radius R and total charge Q. (Use infinity as your reference point).
3. (10 pts.)
Find the capacitance of (a) a parallel-plate capacitor consisting to two
metal plates with surface area A held at a distance d apart, and (b) a
concentric spherical metal shells with radii a and b (b > a).
4. (10 pts.)
Show that, for a metallic sphere which carries a total charge Q, it is
energetically more favorable to have all the charge distributed uniformly on
the surface than uniformly throughout the volume.
5. (13 pts.)
Show that the solution to Laplace's equation in some volume is uniquely
determined if either the potential or the surface charge density is
specified on the boundary surface. This is known as the uniqueness theorem.
6. (20 pts.)
A point charge Q is situated at a distance a from the center of a grounded
conducting sphere of radius R. Let z-axis be along the line joining the
charge Q and the center of the sphere and r, θ are the usual spherical
polar coordinates. Use the method of images to find (a) the potential
V(r,θ) outside the phere, (b) the induced surface charge density on the
sphere as a fubction of θ, (c) the force between the charge Q and the
sphere, and (d) the energy of this configuration.
7. (15 pts.)
Find the potential (a) inside and (b) outside a spherical shell of radius R
with a surface charge density distribution σ(θ) = k*sin^2[θ/2] specified
on its surface.
8. (12 pts.)
An electric dipole consists of two equal and opposite charge ±q separated
by a distance d. Find (a) the approximate potential and (b) the electric
field at points far away from the dipole.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.248.143