As per the syllabus of gondwana university Gadchiroli

1. Uint-III

2. Maxwell’s Equations &
Electromagnetic wave propagation
• Characteristics of electromagnetic Waves
Electromagnetic waves are transvers waves.
Electromagnetic waves are composed of electric
and magnetic fields which are perpendicular to
each other and both fields are perpendicular to
the direction of propagation
Electromagnetic waves can be propagated
without any medium . These waves cannot be
deflected by electric and magnetic field.

3. E.M. waves follows the rule reflection ,
refraction ,transmission ,interference and
diffraction .
E. M. waves can be polarized.
E.M. waves can propagated through the
vaccume with speed of light.
E.M. waves are used in radio,T.V.,cordless
phones, mobiles and remote etc

4. Maxwell’s electromagnetic Equation
Maxwell’s first Equation-
𝛻 X H = j +
𝜕𝐷
𝜕𝑡
Word statement
The electromotive force around a closed
path is equal to the time derivative of the
electric displacement through any surface
bounded by the path.

5. • Physical significance-
1) it is the time dependent equation and
relates the space variation of D or E.
2) It relates the magnetic field vector B with
electric displacement vector D and current
density j .
3) It is the statement Ampere’s law
4) According to this equation magnetic field
vector B can be generated by current density
vector j and time variation of D or E jointly as
well as seperatly.

6. • Maxwell’s Second Equation-
𝛻 X E = -
𝜕𝐵
𝜕𝑡
Word statement-
The electromotive force around a closed path is
equal to the time derivative of the magnetic
displacement through any surface bounded by
the path.

7. • Physical significance
1) It is time dependent equation varying with
time.
2) It relates the space variation of E with time
variation of B
3) It gives the relation between electric field
vector E and magnetic field vector B
4) It is the statement of faradays and lenz’s law
of electromagnetic induction.

8. Maxwell’s Third Equation
• 𝛻. 𝐷 = 𝜌
• World Statement –
It states that the total electric displacement
through the surface enclosing a volume is equal
to the total charge within the volume .

9. • Physical significance-
It is steady state equation independent of
time.
According to this equation the flux lines of
electric force depends upon charge density𝜌.
As 𝛻. 𝐷 = 𝜌 , it signifies that 𝜌 is the charge
density is a scalar quantity.
The positive charge acts as a source and
negative charge as a sink for electric line of
force.

10. • Maxwell’s fourth Equation –
𝛻. 𝐵 = 0
World statement- The net magnetic flux
emerging through a closed surface is zero.

11. • Physical significance –
It is steady state equation independent of
time.
According to this equation , isolated magnetic
poles doesnot exist.
As 𝛻. 𝐵 = 0 , equal number of line of magnetic
force enters as well as leave a given volume.
Lines of magnetic forces are endless i.e. there
is no source and sink for a magnetic line of
force.

12. The Poynting Vector
• The most remarkable characteristics of an
electromagnetic wave is that it transports
energy from one region to another region .
• Energy transfer is describes in terns of the rate
of energy flow per unit area or power per unit
area by a vector ‘P’ called as poynting vector

13. • Definition of poynting vector-
The cross product of the electric field vector E
And the magnetic field vector H is known as
poynting vector P .
Mathematically
poynting vector , P = E X H
Unit
, P = E X H =
𝑣𝑜𝑙𝑡𝑠
𝑙𝑒𝑛𝑔𝑡ℎ
X
𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝑙𝑒𝑛𝑔𝑡ℎ
=
𝑝𝑜𝑤𝑒𝑟
𝐴𝑟𝑒𝑎
=
𝑤𝑎𝑡𝑡𝑠
𝑚𝑒𝑡𝑒𝑟