課程名稱：電磁學上
課程性質：物理系必帶
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）：99/11/18
考試時限：120分鐘（8:10~10:10）
是否需發放獎勵金：是
範圍：Introduction to Electrodynamics 3rd edition CH2.5~CH3.3.1.
1.An inverted hemispherical bowl of rdius R carries a uniform surface charge
density σ.Find the potential difference between the point P and the center.
The point P is located at rhe center point (x=0,y=0,z=R/2) between the north
pole and the center.(10%)
2.A sphere of radius R carries a charge density ρ=kr(k:constant).
(a)Find the total charge Q.(5%)
(b)Find the net force that southern hemisphere exerts on the northern
hemisphere, in terms of R and k.(10%)
(c)If the same charge Q redistributing uniformly on a spherical shell
with radius of R, again find the net force taht southern hemispherical
shell exerts on the northern hemispherical shell, in terms of R and k.(10%)
//↑y ↑y
//│ │←─── a ────→
//├─────┐q ╔═════════════╗
//│a │ ║ ↑ V=V0 ║
//│ │ ║ b ║
//│ │ V=0║ ║V=0
//│ │a ║ ↓ ║
//┼─────┴──→x ╚═════════════╝──→x
V=0/////////////////// V=V1
(Fig.2) (Fig.3)
3.Two semi-infinte grounded conducting planes meet at right angle. There is
a point charge q situated at (x=a,y=a,z=0) as shown in Fig.2.
(a)Find the surface charge densities induced on the two half-planes.(10%)
(b)Find the force exerts on q. (5%)
(c)Calculate the energy of this configuration.(10%)
4.Consider the rectngular region shown in Fig.3 as the cross section of an
enclosure formed by four conducting plates. The left and right plates are
grounded, and the top and bottom plates are maintained at constant
potentials V0 and V1 respectively. Determine the potential inside the
enclosure.(20%)
5.(a)Determine the capacitance per unit length between two long, straight
copper pipes, each of radius R. The axes of the pipes are separated
by a distance 2d.(10%)
[Hint: you should suppose that they respectively carry a line charge
density +λ, -λ and find the potential difference between them. The
results in P2.47 are useful: the equipotential surfaces corresponding
to V0 are circular cylinders, with center at (y0,0) and radius R
(crosses section view), where y0=a*coth(2π*ε0*V0/λ)
R=a*csch(2π*ε0*V0/λ), and 2a is the distance between the two image
charge densities. You can also try other methods that need not use the
result in P2.47]
(b)Find the energy stored per unit length as if there are potentials +V0
and -V0 on the two copper pipes respectively.(10%)
6.A point charge q is located inside and at distance a from the center of
a grounder spherical conducting shell of radius R (where R>a). Use the
method of images and the law of cosines ot determine:
(a)the potential distribution inside the shell,(10%) and
(b)the surface density σ induces on the inner surface of the shell.(10%)
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