课程名称：电磁学上 课程性质：物理系必带 课程教师：王立民 开课学院：理学院 开课系所：物理系 考试日期：（年月日）：99/11/18 考试时限：120分钟（8:10~10:10） 是否需发放奖励金：是 范围：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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