Electromagnetic Fields : Maxwell's, Poisson's & Laplace equations

By Yash Bansal|Updated : October 14th, 2021

In this article, you will find the Study Notes on Maxwell’s Equations which will cover the topics as Maxwell's Equations in Time-varying Field, comparison in static electric field and magnetic field, and some key relations.

 

                                                                                                                                                                 

In this article, you will find the Study Notes on Maxwell’s Equations which will cover the topics as Maxwell's Equations in Time-varying Field, comparison in static electric field and magnetic field, and some key relations.

Maxwell’s Equations in Time-Varying Field

  • Maxwell's equations in point form
    1.  (Faraday’s Law)
      image001
    2. (Modified Ampere’s circuital Law)
      image002
    3. (Gauss’s Law)
      image003
    4. (Non-existence monopole or Gauss’s law of magnetostatics)
      image004

      Maxwell's equations in integral form
      image005
      image006
      image007
      image008

      Key Points

      • For static fields (or non-time varying fields)
        image009
        The basic equations of electromagnetism are the four Maxwell Equations and the Lorentz force law. In principle, these, together with Newton’s second law of motion are enough to completely determine the motion of an assembly of charges given the initial positions and velocities of all the charges. Maxwell’s equations are, 
        image012
        image013
        image014
        image015
        Here, image016 are the electric and magnetic fields respectively. The sources for the fields are the volume charge density ρ and the current density. The two parameters in these equations are the permittivity of free space image019 and the permeability of free space image020. The vector, differential-operator in these equations is defined as
      • image021

        these equations can be used to determine the fields if the charge and current densities are known. Once the fields are known, the force felt by a given charge q moving with velocity  is given by the Lorentz force law,

        image023

        In principle, Equations (1)-(5) constitute all electromagnetic. However, in practice, the charge and current densities associated with matter are too complicated to specify and so a phenomenological means of dealing with the matter is often introduced.

      Maxwell Equation for Time-Varying Field : 

              Maxwell Equation for Time-Varying Field in Free Space

       

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Yash BansalYash BansalMember since Nov 2018
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