Electromagnetic Fields - Maxwell's, Poisson's & Laplace equations Complete Study Notes

By Vishnu Pratap Singh|Updated : March 8th, 2022

Complete coverage of the UPPCL AE Exam syllabus is a very important aspect for any competitive examination but before that important subjects and their concept must be covered thoroughly. In this article, we are going to discuss the fundamental of Maxwell's, Poisson's & Laplace equations which is very useful for UPPCL AE Exams.

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
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      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 : 
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              Maxwell Equation for Time-Varying Field in Free Space

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