完全版电磁场与电磁波习题.doc

2.4 Verify the Pythagorean theorem. In other words, show that if and only if is perpendicular to .2.8 Show that 2.17 Express that position vector in the spherical coordinate system.2.20 and are two vectors at point and , respectively. Determine (a) ,(b) ,(c) , (d) the unit vector perpendicular to and (e) the angle between and 2.40 Show that (a), and (b) in the cylindrical coordinate system.2.41 Show that in the cylindrical coordinate system.2.42 If the electric field intensity in space is given as, find and.2.44 Given, verify the divergence theorem when the region is bounded by a cylinder and the planes at and .2.37 Using the rectangular coordinate system, verify that (a) and (b) 2.38 In electromagnetic fields, we will define the electric field intensityas a negative gradient of a scalar function; i.e. We will also define the volume charge distribution as, where is the permittivity of free space. Determineandif (a) in cylindrical coordinates, whereandare constants, (b) in spherical coordinates, andin spherical coordinates.2.48 Verify Stokes theorem over a hemispherical surface atandfor a function .能够给出最后计算结果的，以后都要给出最后计算结果而不是表达式)3.6 An electron is circling around nucleus of a hydrogen atom at a radius of 0.05nm. Determine the angular velocity and the time period of the electron. 3.8 The surface charge density on a quarter-disc in the first quadrant is. If the radius of the disc is a, find the E field at a point at.3.13 Two straight uniformly charged lines are extending along the z axis fromto. One line carries a charge distribution ofand is situated at, and the other line is atand has a charge distribution of. Determine the E field at appoint on the x axis at.3.14 Three infinite electric sheets carrying uniform charge densities of 2,-3 and 0.5are each separated by a 1-mm air gap, as shown in figure. Find the electric field intensity everywhere in space. 3.15 An arc radius 0.2m lies in theplane and extends from. It has a charge distribution of. Determine thefield at (a) a point, and (b) the origin.3.16 A finite line extends fromtoand carries a charge distribution of. Determine thefield at a point 2 meters away from the line in theplane.3.25 A spherical volume of radius b supports a charge distribution of everywhere except at . Determine the electric flux density in the region (a), and (b)5.5 Find the magnetic flux density at point P in Figure 5.5.Figure 5.53.41 A long coaxial cable consists of an inner conductor of radius a and an outer conductor of inner radius b and outer radius c. The inner conductor carries a uniform surface charge distribution s. Find the E field at any point in space when (a) the outer conductor is not grounded, and (b) the outer conductor is grounded. (考考大家对静电平衡的感觉)3.42 A uniform charge density s exists on the surface on f an infinitely long metal cylinder of radius a. It is surrounded by a concentric dielectric of inner radius a and out radius b. Compute (a) D, E, and P at all points in space, (b) the bound charge densities, and (c) the energy density in the system. （c部分暂缓）3.43 Find an expression forin a charge-free but nonhomogeneous medium.3.44 The permittivity of a dielectric medium is given as whereand n are constants. If the electric field intensity in the medium has on a z component, show that, where E is the magnitude of the electric field intensity.3.45 A metal sphere of radius b has uniform surface charge distribution. The permittivity of the surrounding region varies as. Find (a) D, E, and P everywhere in space, (b) the bound charge densities, and (c) the energy density, and (d) show that the potential in the dielectric region is , where Q is the total charge on the sphere. (c,d 部分暂缓)5.32 A coaxial cable consists of a long cylindrical conductor of radius a surrounded by a cylindrical shell of inner a radius b and outer radius c. The inner conductor and the outer shell each carry equal and opposite currents I uniformly distribution through the conductors. Obtain expressions for the magnetic field intensity in each of the regions (a), (b) , (c), and (d)5.34 A current I flows in a thin wire bent into a circle of radius b. The axis of the circular loop coincides with the z axis. Compute along the z axis form to. What do you conclude from your answer?5.35 The magnetic flux density in a region1, is . If marks the boundary between regions 1 and 2, determine the magnetic flux density in region 2. Consider region1 as free space; regions 2 has a relative permeability of 100.5.36 A current sheet of separates two regions at. Region 2, has a magnetic field intensity ofand a relative permeability of 200. If region 1, has a permeability of 1000, determine the magnetic field intensity in this region.5.37 Refer to Problem 5.35. Compute the magnetization vector in each region. What the bound volume and surface current densities in each region. 由于题目都是类似的，故没有写题目，仅仅画图！3.58 Capacitance?3.59 Capacitance?3.60 Capacitance?(a=1cm, b=1.5cm)3.61 Capacitance? (红色为极板)（xoy方向俯视图，z方向高度为h=10cm）3.62 Capacitance?（球形）7.13 Three coils with 100, 150, and 200 turns are tightly and closely wound on a common magnetic circuit of 40cm2 in cross section and 80cm in length. Determine (a) the self-inductance of each coil, (b) the mutual inductance between any two coils. Assume the relative permeability of the magnetic material as 500.3.63 A large spherical cloud of radius b has a uniform volume charge distribution of v. Calculate and sketch the potential distribution and the electric field intensity at any point in space using Poissons and Laplaces equations.3.66 Determine the potential distribution in a coaxial cable when the inner conductor of radius 10cm is at a potential of 100v and the outer conductor radius 20cm is grounded. The space between the conductors is filled with two concentric dielectrics. The dielectric constant is 3 for the inner dielectric and 9 for the outer dielectric. The dielectric interface is at a radius of 15cm. Determine (a) the potential distribution, (b) the D and E field in each region, (c) the surface charge density on the inner conductor, and (d) the capacitance of the 100-meter-long cable.3.67 Calculate the capacitance of two spherical shells of radii a and b using Laplaces equation. The inner shell is at a potential of V0, and the outer shell is grounded. What is the surface charge density on the inner shell? Obtain the expression for the capacitance of the system.3.71 Two infinite grounded metal plates parallel to the z axis are at. A charge of 500nC is placed atm. Calculate the potential function and the electric field intensity at m. Assume that the medium between the plates is free space.7.1 Two conducting bars are sliding over two stationary conductors, as show in figure. What is the induced current in the closed loop thus formed when its resistance is 12?7.29 If the electric field intensity in a source-free, dielectric medium is given as,Determine the magnetic field intensity using Maxwells equation from Faradays law. What is the displacement current density in the medium? (此题和应该算已知)7.30 If the magnetic field intensity in a source-free, dielectric medium is given as,Determine the electric field intensity using Maxwells equation from Amperes law. What is the displacement current density in the medium?7.31 Determine the condition that must be satisfied for the existence of the electric field intensity as given in Problem 7.29.7.32 Can the magnetic field intensity as given in Problem 7.30 exist? If yes, what must be the condition? If no, explain why the fields cannot exist.7.33 Ifin a dielectric medium, show that the electric energy density is equal to the magnetic energy density. Also compute (a) the Poynting vector, (b) the average power density, and (c) the time-average values of the energy densities. (b和c的差别一个是数值上的平均值，一个是对时间的平均值)7.34 Compute the tine-average electric and magnetic energy densities for the fields given in Problem 7.29.7.35 Compute the tine-average electric and magnetic energy densities for the fields given in Problem 7.307.49 For electromagnetic fields to exist in a linear, homogeneous, isotropic, source-free conductive region, show that the E field must satisfy the following equation:.7.50 For electromagnetic fields to exist in a linear, homogeneous, isotropic, source-free conductive region, show that the H field must satisfy the following equation:7.51 In a dielectric medium (and) the E and H fields are given as follows: and Using phasor analysis, determine (a)and, (b)the direction of power flow, and (c) the average power crossing the surface area bounded by the corners of triangle at (2,0,0)m, (2,4,0)m, and (2,4,2)m.（7.34和7.35算思考题）8.4 Show that the electric field intensity as given by is a valid solution of the wave equation in a dielectric medium. Also determine (a) the electric constant of the medium assuming that, (b) the velocity of propagation, (c) the magnetic field intensity, (d) the intrinsic impedance, (e) the wavelength, and (f) the average power density.8.6 The electric field intensity of a uniform plane wave in free space is given by. Determine (a) the phase constant, (b) the magnetic field intensity, (c) the wavelength, (d) the average power density in the medium, (e) the average energy density in the electric field, and (f) the average energy density in the magnetic field.8.10 A uniform plane wave at a frequency of 100MHz propagates in the z direction in a conducting medium characterized by and. Determine,and (不会把前面的取正切吧，否则晕倒). If the maximum value of the electric field intensity in the y direction is and occurs at z=0 and t=0, write expressions for the E and H field. Obtain a general expression for the power density in the medium. What is the total current density in the medium?8.11 A glass material is coated with silver () to make it a good conductor at 2.4GHz. What is the surface resistance of the coating?8.14 An antenna just beneath the surface of a most soil (,) is transmitting a signal at 60MHz. Assuming that signal propagates as a uniform plane wave, a receiver buried in the soil receives the signal with a strength of 1/10 of its original value. Compute the distance of the receiver.8.15 The electric field intensity of a wave in a region is given by; determine the polarization of the wave.8.16 Find the polarization of a wave if the electric field intensity is given by.8.22 An electromagnetic wave propagates in a dielectric medium withalong the x direction. It strikes another dielectric medium withat x=0. If the incoming wave is polarized in the z direction, has a maximum value of 250mV/m at the interface, and has an angular frequency of 300Mrad/s, determine (a) the reflection coefficient, (b) the transmission coefficient, and (c) the power densities of the incident, reflected, and transmitted waves.8.21 If we define the standing wave ratio (SWR) as the ratio of the maximum to the minimum values of the total E field in medium 1, show that whereis th