maxwell equation cylindrical coordinates

Time-harmonic data is the large class of physical quantities that vary periodically with time. Also, they can characterize a simple medium mathematically with a permittivity, e, and a permeability, µ, as follows:įor free space such as air, µ = µ 0 = 4p10 -7 H/m and e = e 0 = 8.85 x 10 -12 F/m Maxwell's Equations for Time-Harmonic Fields (12) Constitutive RelationsĬonstitutive relations can provide physical information for the environment in which electromagnetic fields occur, such as free space, water, or composite media. In fact, to solve electromagnetic field problems, it is essential to assume that the sources J and r v are given and satisfy the continuity equation. This law is also known as the continuity law of electric charge. The conservation law means that the rate of transfer of electric charge out of any differential volume is equal to the rate of decrease of total electric charge in that volume. The Maxwell equation (55) can be presented using the vector identity (57) and multiplying both sides by ? as follows:īeing replaced with equation 54, the conservation law for current and charge densities is defined as the following: Where: (60) Conservation Law of Electric Charge Some useful vector identities are as follows: (12)

The operator as a vector is only permissible in rectangular coordinates. In addition, if f ( x, y, z) is a scalar function of the coordinates, the operation ? f is called the gradient of f. The former is a vector and the latter is a scalar. If A and B are vectors, the operation ? x A is called the curl of A, and the operation ? x B is called the divergence of B. Where = unit vectors along the x, y, and z axes The symbol ? in Maxwell's equations represents a vector partial-differentiation operator as following, In order to understand concepts of Maxwell's equations, some definitions and vector identities are described. The equations express the physical laws governing the E, D, H, and B fields and the sources J and r v at every point in space and at all times.

J and ? v are the sources generating the electromagnetic field. The fundamental theory of electromagnetic fields is based on Maxwell's equations governing the fields E, D, H, and B: = magnetic flux density (webers per square meter, wb/m 2) = magnetic field strengths (amperes per meter, Am/m) = electric flux density (coulombs per square meter, C/m 2) = electric field strength (volts per meter, V/m) In the study of electromagnetics, the four vector quantities called electromagnetic fields, which are functions of space and time, are involved: (2) E The following describes the basic theories and concepts of electromagnetics and the TLE. The new approach for calculating dielectric constant in this project utilizes the transmission line equation (TLE). LTPP Computed Parameter: Moisture Content Appendix A.

Maxwell equation cylindrical coordinates