课程名称︰电磁学上 课程性质︰系必修 课程教师︰陈正弦 开课学院：理学院 开课系所︰物理学系 考试日期（年月日）︰2008/11/06 考试时限（分钟）：120 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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. --

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