Generally a light wave is called electromagnetic wave means its constituted of both the electric and magnetic field vector (complementary to each other) and when it travels through different mediums such as free space,isotropic,dielectric,conducting mediums ,the various physical properties of it, changes.
Maxwell introduced electromagnetic theory to understand the behaviour of light as it travels through free space and an isotropic dielctrics.Maxwell gave the mathematical form to the existing Gauss,Ampere and Faradey’s laws.
The four Maxwell equations unified together formed the new branch of “Electromagnetic Field Theory” which says that “Light is an electromagnetic wave moving through various media.This theory is dependent upon three fundamental mathematical operations which are Gradient, Divergence and Curl.Without understanding these three fundamentals it is difficult to solve and understand Maxwell’s equations.
Gradient means rate of changes in a scalar function in a specified direction .Gradient measures the scalar function and its itself a vector quantity which has magnitude as the power or intensity of particular vector at a definite point and it follows the direction which has maximum rate of changes means along the normal because perpendicular distance is the shortest distance, so it has maximum rate of changes.
To understand the Gradient in a better way please must watch this video…
Divergence means the flux passing through unit area which may be increasing (positive),decreasing (negative) or remains as it is (zero) accoding to the presence of source or sink at that particular area,There can be so many examples to understand the Divergence which are widely disscused in this video alongwith some numericals .So please must watch this video to understand divergence properly.
Now curl is a mathemathical operator which operates upon a vector quantity and gives a vector quantity after operation.It measures the rotation of vector field. Since its a vector quantity therefore it has magnitude as maximum rotation of vector field and direction just normal to the flow of field or we can say it follows right hand thumb rule. How to take curl in the form of cartesian co ordinates and how it can apply on a vector field, these all queries are covered in this video.So to understand properly the quantity Curl please watch this video…….
In this way all three mathematial functions gradient, divergence and curl can be understood in a layman term that if we consider a toilet bowl then when we start flush then as much water comes from tank it is divergence, as the pressure of water chnages point to point, it is gradient and as much water rotate in that particular area, that shows its curl.
