Maxwells Equations: Maxwell’s equations are a set of four partial differential equations that describe the behavior of electric and magnetic fields in space. These equations were first formulated by James Clerk Maxwell in the 19th century and are the foundation of the study of classical electromagnetism.

Maxwells Equations

The four equations are:

• Gauss’s law for electric fields: This equation relates the electric flux through a closed surface to the electric charge enclosed within the surface. It is given by:

∇ ⋅ E = ρ/ε₀

Where,

• E is the electric field,
• ρ is the electric charge density, and
• ε_0 is the permittivity of free space.

2. Gauss’s law for magnetic fields: This equation states that the magnetic flux through any closed surface is zero. It is given by:

∇ ⋅ B = 0

Where, B is the magnetic field.

3. Faraday’s law of electromagnetic induction: This equation describes the relationship between a changing magnetic field and an induced electric field. It is given by:

∇ × E = – ∂B/∂t

Where, E is the electric field and B is the magnetic field.

4. Ampere’s law with Maxwell’s correction: This equation describes the relationship between the magnetic field and the electric current. It is given by:

∇ × B = μ₀(J + ε₀∂E/∂t)

Where,

• B is the magnetic field,
• J is the electric current density,
• E is the electric field,
• μ₀ is the permeability of free space, and
• ε₀ is the permittivity of free space.

These four equations together describe the behavior of electric and magnetic fields in space, and their interdependence leads to the propagation of electromagnetic waves. The equations are used extensively in the design of electronic devices, communication systems, and many other applications in electrical engineering, physics, and related fields.

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By Team Learning Mantras