高等电磁理论复习题.doc

1. Derive the differential form of the continuity equation from Maxwell’s equations. 2. Derive the integral forms of Maxwell’s equations and the continuity equations, from the corresponding ones in differential form 3. The electric flux density inside a cube is given by (a) , (b) . Find the total electric charge enclosed inside the cubical volume when the cube is in the first octant with three edges coincident with the x, y, z axes and one corner at the origin. Each side of the cube is 1m. 4. The electric field inside a circular cylinder of radius a and height h is given by where c and b are constants. Assuming the medium within the cylinder is free space, find the total charge enclosed within the cylinder. 5. The instantaneous electric field inside a source-free, homogeneous, isotropic, and linear medium is given by Determine the relations between A and B. 6. The magnetic flux density produced on its plane by a current-carrying circular loop of radius a = 0.1 m, placed on the xy plane at z = 0, is given by Wb / m2 where ρ is the radial distance in cylindrical coordinates. (a) Find the total flux in the z direction passing through the loop. (b) Find the electric field at any point ρ within the loop. 7. The instantaneous magnetic flux density in free space is given by where Bx and By are constants. Assuming there are no sources, determine the electric displacement current density. 8. The displacement current density within a source-free cube centered about the origin is given by Each side of the cube is 1 m and the medium within it is free space. Find the displacement current leaving, in the outward direction, through the surface of the cube. 9. The time-harmonic complex electric field radiated in free space by a linear radiating element is given by where and are unit vectors in the spherical direction r and θ, E0 is a constant, and . Determine the corresponding spherical magnetic field components. 10. A time-harmonic electromagnetic field traveling in free spac