Maxwell’s Third Equation – Derived from Faraday’s law of Induction
According to Faraday’s Law of Induction , a change in magnetic field induces an electromotive force which is called emf in short. This generates an electric field.
The direction of the EMF tries to oppose the change. The electric field arising from a changing magnetic field represents field lines that form closed loops that do not have any beginning or end.
From Faraday’s law of Induction
∮ [Tex]\overrightarrow{\rm E} [/Tex]. dl = − ∬ d[Tex]\overrightarrow{\rm B} [/Tex]/ dt. ds —-(1)
Applying Stokes Theorem,
∮ [Tex]\overrightarrow{\rm E} [/Tex] .dl = ∬ (∇ × [Tex]\overrightarrow{\rm E} [/Tex]) .ds —-(2)
From equations (1) and (2) we get,
∬ ( ▽× [Tex]\overrightarrow{\rm E} [/Tex]) ds = ∬ – [Tex]\overrightarrow{\rm B} [/Tex]/dt .ds
▽× [Tex]\overrightarrow{\rm E} [/Tex] = – [Tex]\overrightarrow{\rm B} [/Tex]/dt (Maxwell’s Third 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