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Poynting Theorem Chapter 8, Page 346, Griffith

Poynting Theorem Chapter 8, Page 346, Griffith. Lecture : Electromagnetic Power Flow. Statement: Poynting’s Theorem “Conservation of Energy”.

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Poynting Theorem Chapter 8, Page 346, Griffith

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  1. Poynting TheoremChapter 8, Page 346, Griffith Lecture : Electromagnetic Power Flow

  2. Statement: Poynting’s Theorem“Conservation of Energy” “The work done on the charges by the electromagnetic force is equal to the decrease in energy stored in the field, less the energy that flowed out through the surface”

  3. Total energy stored in Electromagnetic fields is Suppose we have some charge and current configuration, produces fields E and B at time t. Work done (by applying Electromagnetic forces ) on a charge q isgiven by Rate of work done on charges and current available in the system

  4. Using maxwell’s equations ? Can we obtain • Maxwell’s curl equations in differential form • Recall a vector identity • Furthermore,

  5. Derivation of Poynting’s Theorem in the Time Domain (Cont’d) • Integrating over a volume V bounded by a closed surface S, we have • Using the divergence theorem, we obtain the general form of Poynting’s theorem

  6. Derivation of Poynting’s Theorem in the Time Domain (Cont’d) • Note that • Hence, we have the form of Poynting’s theorem valid in simple, lossless media:

  7. Physical Interpretation of the Terms in Poynting’s Theorem • Hence, the terms represent the total electromagnetic energy stored in the volume V. • The term represents the flow of instantaneous power out of the volume V through the surface S. • The term represents the total electromagnetic energy generated (Rate of work done) by the sources in the volume V.

  8. Rate of work in the system System of q and I Applied Lorentz force Power flow Rate of decrease in stored energy

  9. Differential form of Poynting’s Theorem Shows Conservation of Energy

  10. Poynting Vector in the Time Domain • We define a new vector called the (instantaneous) Poynting vector as • The Poynting vector has the same direction as the direction of propagation. • The Poynting vector at a point is equivalent to the power density of the wave at that point. • The Poynting vector has units of W/m2.

  11. Boundary conditions, Page 333, Ch. 7 • If there is no free charge or free current at the interface of two medium, then E┴ Incident E E// Reflected Medium-1(ε1 , µ1) Medium-2(ε2 , µ2) Refracted

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