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Mr. HIMANSHU DIWKARAssistant Professor

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Electromagnetic wave propagation

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Outline• Maxwell’s Equation Review• Helmholtz Equation• Propagation constant• Properties of Electromagnetic Waves• Plane Wave• Uniform Plane Wave• Uniform Time-harmonic plane wave• Wave characteristic• In Lossy Media• In Lossless Media

• Wave Propagation in Free Space• Pointing Theorem and Pointing Vector

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This lecture on Electromagnetic Waves and subsequent lectures demands that you must have rigorous review of Electrostatic, Magneto-statics and Vector identities.

Therefore, sit in class after reviewing the aforementioned material to really understand Electromagnetic waves as fun!!

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Region 1Sources J,

Region 2Source free region

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Pointing theoremIn electrodynamics, Poynting's theorem is a statement of conservation of energy for

the electromagnetic field, in the form of a partial differential equation, due to the British physicist

John Henry Poynting.

The theorem states– the time rate of change of electromagnetic energy within V plus the net energy

flowing out of V through S per unit time is equal to the negative of the total work done on the charges

within V.

A second statement can also explain "The decrease in the electromagnetic energy per unit time in a

certain volume is equal to the sum of work done by the field forces and the net outward flux per unit

time".

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• Consider first a single particle of charge q traveling with a velocity vector v. Let E and B be electric and magnetic fields external to the particle; i.e., E and B do not include the electric and magnetic fields generated by the moving charged particle. The force on the particle is given by the Lorentz formula

F = q(E + v×B)

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• The work done by the electric field on that particle is equal to qv·E. The work done by the magnetic field on the particle is zero because the force due to the magnetic field is perpendicular to the velocity vector v.• For a vector field of current density J the work done on the charges

within a volume V is∫VJ·EdV

• It is convenient to define a vector P, known as the Poynting vector for the electrical and magnetic fields, such that

P = (c/4π)(E×H)

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Thank you

HIMANSHU DIWAKAR