Physics: Electromagnetism
Maxwell’s Equations
Introduction
Maxwell’s equations are a set of four equations that describe the behavior of electric and magnetic fields. They are named after James Clerk Maxwell, who formulated them in 1861.
The four equations are:
- Gauss’s Law for Electricity
- Gauss’s Law for Magnetism
- Faraday’s Law of Induction
- Ampère’s Law with Maxwell’s Addition
These equations are fundamental to the study of electromagnetism and have wide-ranging applications in physics and engineering.
On a separate note, we also have the Lorentz force law in electromagnetism, which is closely related but not part of Maxwell’s equations. So, we won’t talk about that.
Maxwell’s Equations (Integral Form)
Gauss’s Law for Electricity
Gauss’s Law for Electricity states that the electric flux through a closed surface is proportional to the total charge enclosed by the surface. Mathematically, it is expressed as:
- E represents the electric field.
- dA is an infinitesimal…
