 # Maxwell Equations

Maxwell equations mainly give us the idea about how the electric and magnetic field interacts with each other. There are some fundamental relationships which explain how the magnetic and electric field generated and interacted with each other. Maxwell equations mainly consist of a set of four laws such as Gauss’s electric field law, Gauss’s magnetic field law, Faraday’s law, Ampere Maxwell law. Maxwell Equations

## Gauss’s Electric Field Law

This law mainly defines the relationship between the positive or negative charge and the electric field. The electric field is mainly introduced as an electrostatic field in Gauss’s electric field law. This law describes how the electrostatic field changes and behaves with the charge distribution within the circuit. This law also relates to the electric flux passing through the surface which contains the positive or negative charge. The law states that “The electric field flux passing through a closed surface is proportional to the charge contained within that surface”.  This defines the total flux passing through a closed surface is equal to the total charge contained by the surface.

### Gauss’s Magnetic Field Law

Gauss’s magnetic field law describes the relationship between the magnetic poles and the magnetic field. The law states that “The total magnetic flux passing through a surface is equal to zero”.

All the electrical machines, transformers, generators work in the principle of faraday’s law. It defines that a time-varying magnetic field is always connected with a time-varying electric field. The law states that “A changing magnetic flux within a surface induces an electromotive force or EMF and induced current. The induced current creates a circulating electric field”.

#### Ampere Maxwell Law

This law mainly describes that a varying electric field creates a magnetic field. First Ampere considers the current as a steady current but Maxwell’s letter corrects it and considers the current as induced time-varying currents. The law states that “Changing current or electric flux through a surface produces a changing magnetic field”. This law is based on the Ampere circuit law.

Maxwell equations are all related to a unique velocity c or the speed of light. Hence all the Maxwell equations are correct in terms of Einstein’s special theory of relativity. Gauss’s electric field law also indicates that the electric field direction is always perpendicular to the velocity direction or the light direction.

Q.1 What is the main importance of Maxwell equations?

Answer: Maxwell equations give us the idea that a changing magnetic field always induces an electric field and a changing electric field always induces a magnetic field.

Q.2: What are the main applications of Maxwell equations?

Answer: The main applications of Maxwell equations are we can calculate static electric field in a vacuum, we can calculate static magnetic field in a vacuum, it gives us the idea about electric circuits.

Q.3: Which produces magnetic field according to Maxwell equations?

Answer: According to Maxwell equations the displacement current can produce a magnetic field. Earlier it was believed that only conduction current could induce magnetic field but Maxwell Ampere’s law corrects it.

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