1. TIME VARYING FIELDS AND MAXWELL’S EQUATION
PREPARED AND COMPILED BY:
NAME: KHUSHBOO .I. RAJPUROHIT
ENROLLMENT NO.:
SEMESTER: 5th
BRANCH: ELECTRONICS AND COMMUNICATION
GUIDED BY:
Asst.Prof. CHIRAG PARMAR

2. TIME VARYING FIELDS
Time varying electric field can be produced by time varying magnetic field and
Time varying magnetic field can be produced by time varying electric field.
The equations describing the relation between changing electric and magnetic fields are known as MAXWELL’S EQUATION
Maxwell’s equation are extensions of the known work of Gauss ,Faradays and Ampere.
There are two forms of Maxwell’s equation namely:
1. Integral form.
2. Differential or point form.

3. Faraday's Law
Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc.
Faraday's law is a fundamental relationship which comes from Maxwell's equations. It serves as a succinct summary of the ways a voltage may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

5. Lenz’s Law
When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. In the examples below, if the B field is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to try to keep it constant.

6. Faraday's Law
A nonzero value of emf may result from of the situations:
1 – A time-changing flux linking a stationary closed path
2 – Relative motion between a steady flux and a closed path
3 – A combination of the two

9. Displacement Current & Maxwell’s Equations

14. Maxwell’s equations: Gauss’s law

15. Maxwell’s equations: Gauss’ law for magnetism

16. Maxwell’s equations: Faraday's law

17. Maxwell’s equations: Ampere’s law

18. Poynting’s Theorem
It is frequently needed to determine the direction in which the power is flowing. The Poynting’s Theorem is the tool for such tasks.
We consider an arbitrary shaped volume:
We take the scalar product of E and subtract it from the scalar product of H.

19. Application of divergence theorem and the Ohm’s law lead to the PT:
Here
is the Poynting vector – the power density and the direction of the radiated EM fields in W/m2.

20. Poynting’s Theorem
The Poynting’s Theorem states that the power that leaves a region is equal to the temporal decay in the energy that is stored within the volume minus the power that is dissipated as heat within it – energy conservation.
EM energy density is
Power loss density is
The differential form of the Poynting’s Theorem:

21. SUMMARY

22. REFERENCES

23. THANK YOU