Maxwell’s Second Equation – Derived from Gauss’ law of Magnetism
According to Gauss’ law of Magnetism, magnetic field flux through any closed surface is zero which is equivalent to the statement that magnetic field lines are continuous. They have no beginning or end. Thus any magnetic field line entering the region enclosed by the surface must leave it too.
From Gauss’s Law of Magnetism
∯ [Tex]\overrightarrow{\rm B} [/Tex]. ds = 0 —-(1)
Applying divergence theorem,
∯ [Tex]\overrightarrow{\rm B} [/Tex]. ds = ∭ ∇. [Tex]\overrightarrow{\rm B} [/Tex] dv —-(2)
From equations (1) and (2) we get,
∭ ∇. [Tex]\overrightarrow{\rm B} [/Tex] dv = 0
Here to satisfy the above equation we can either have
∭ dv= 0 or ∇. [Tex]\overrightarrow{\rm B} [/Tex] = 0
Since the volume of any body or object can never be zero. We get our Second Maxwell Equation,
∇. [Tex]\overrightarrow{\rm B} [/Tex] = 0 (Maxwell’s Second 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