Electrodynamics can be summarized into four basic equations, known as Maxwell’s equations.

**Maxwell’s equations in**** ****integral form**

Electrodynamics can be
summarized into four basic equations, known as Maxwell’s equations. These
equations are analogous to Newton’s equations in mechanics. Maxwell’s equations
completely explain the behaviour of charges, currents and properties of
electric and magnetic fields. These equations can be written in integral form
(or integration form) or derivative form (or differentiation form). The
differential form of Maxwell’s equation is beyond higher secondary level
because we need to learn additional mathematical operations like curl of vector
fields and divergence of vector fields. So we focus here only in integral form
of Maxwell’s equations:

1. First equation is
nothing but the Gauss’s law. It relates the net electric flux to net electric
charge enclosed in a surface. Mathematically, it is expressed as

where *E* is the
electric field and Q_{enclosed} is the charge enclosed. This equation
is true for both discrete or continuous distribution of charges. It also
indicates that the electric field lines start from positive charge and
terminate at negative charge. This implies that the electric field lines do not
form a continuous closed path. In other words, it means that isolated positive
charge or negative charge can exist.

2. Second equation has
no name. But this law is similar to Gauss’s law in electrostatics. So this law
can also be called as Gauss’s law in magnetism. The surface integral of
magnetic field over a closed surface is zero. Mathematically,

where is the magnetic field. This equation implies that the magnetic lines of force
form a continuous closed path. In other words, it means that no isolated
magnetic monopole exists.

3. Third equation is
Faraday’s law of electromagnetic induction. This law relates electric field
with the changing magnetic flux which is mathematically written as

where is the electric field. This equation implies that the line integral of the
electric field around any closed path is equal to the rate of change of
magnetic flux through the closed path bounded by the surface. Our modern
technological revolution is due to Faraday’s laws of electromagnetic induction.
The electrical energy supplied to our houses from electricity board by using
Faraday’s law of induction.

4. Fourth equation is
modified Ampere’s circuital law. This is also known as Ampere – Maxwell’s law.
This law relates the magnetic field around any closed path to the conduction
current and displacement current through that path.

where is the magnetic field. This equation shows that both conduction and also
displacement current produces magnetic field. These four equations are known as
Maxwell’s equations in electrodynamics. This equation ensures the existence of
electromagnetic waves. The entire communication system in the world depends on
electromagnetic waves. In fact our understanding of stars, galaxy, planets etc
come by analysing the electromagnetic waves emitted by these astronomical
objects.

Tags : Electromagnetic Waves , 12th Physics : Electromagnetic Waves

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12th Physics : Electromagnetic Waves : Maxwell’s equations in integral form | Electromagnetic Waves

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