# Maxwell’s Equations Study Notes of Electrical Engineering for GATE EC Exam 2022

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Maxwell’s Equations Study Notes of Electrical Engineering for GATE EC Exam 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.

Table of content

## Maxwell’s Equations in Time-Varying Field

• Maxwell’s equations in point form
2.  (Modified Ampere’s circuital Law)
3.  (Gauss’s Law)
4.  (Non-existence monopole or Gauss’s law of magnetostatics)
• Maxwell’s equations in integral form

## Key Points

• For static fields (or non-time varying fields)

• For the time-harmonic field Replace the differentiation  and replace the integration
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,
Here,  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  and the permeability of free space . The vector, differential-operator in these equations is defined as
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,
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 Static Field

Maxwell Equation for Time-Varying Field in Free Space
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