TIME VARYING FIELDS AND MAXWELL’S EQUATION PREPARED AND COMPILED BY: NAME: KHUSHBOO .I. RAJPUROHIT ENROLLMENT NO.: 130020111029 SEMESTER: 5th BRANCH: ELECTRONICS AND COMMUNICATION GUIDED BY: Asst.Prof. CHIRAG PARMAR

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.

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.

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.

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

Displacement Current & Maxwell’s Equations

Maxwell’s equations: Gauss’s law

Maxwell’s equations: Gauss’ law for magnetism

Maxwell’s equations: Faraday's law

Maxwell’s equations: Ampere’s law

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.

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.

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:

SUMMARY

REFERENCES https://www.google.co.in/search?q=maxwells+equation&oq=maxwells+equation&aqs=chrome..69i57.6875j0j7&sourceid=chrome&es_sm=93&ie=UTF-8 http://hyperphysics.phyastr.gsu.edu/hbase/electric/maxeq.html http://cms.szu.edu.cn/emc/PPT/7Time-varing%20Fields%20and%20Maxwell%20equations.pdf http://www.slideshare.net/jayaraju_2002/time-varying-fields-and-maxwells-equations http://www.rpi.edu/dept/phys/Courses/ppd1050/Lecture23.ppt

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