Maxwell’s First Equation – Derived from Gauss’ law of Electrostatics
Gauss’s law for electricity states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. Here, the electric flux in an area can be defined as the electric field multiplied by the area of the surface projected in a plane and perpendicular to the field.
As per the Gauss’s Law of Electrostatics
∯ [Tex]\overrightarrow{\rm E} [/Tex].ds = Q/ε0 —-(1)
Applying divergence theorem,
∯ [Tex]\overrightarrow{\rm E} [/Tex]. ds = ∭ ∇. [Tex]\overrightarrow{\rm E} [/Tex] dv —-(2)
From equations (1) and (2) we get,
∭ ∇. [Tex]\overrightarrow{\rm E} [/Tex] dv = Q /ε0 dv
we need to define charge as the integral of volume charge density Q = ∭v ρ dV
∇. [Tex]\overrightarrow{\rm E} [/Tex] = ρ /ε0 (Maxwell’s First Equation)
Maxwell’s Equations in Electromagnetism
Maxwell’s Equations are a set of four equations proposed by mathematician and physicist James Clerk Maxwell in 1861 to demonstrate that the electric and magnetic fields are co-dependent and two distinct parts of the same phenomenon known as electromagnetism.
These formulas show how variations in the quantity or velocity of charges can impact magnetic and electric fields. Maxwell went on to establish that light is an electromagnetic wave caused by oscillations in the electric and magnetic fields. Maxwell’s equations give a mathematical model for the operation of all electronic and electromagnetic devices, ranging from power generation to wireless communication.
Table of Content
- What are Maxwell’s Equations of Electromagnetism?
- Maxwell’s First Equation
- Maxwell’s Second Equation
- Maxwell’s Third Equation
- Maxwell’s Fourth Equation
- Applications of Maxwell Equations