Electromagnetic Field Energy.
The energy of the electromagnetic field enclosed inside a certain volume V, bounded by a closed surface S, is determined by the volume energy density of the electric and magnetic fields
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To determine the rate of the energy variation in time dependent electromagnetic field , it is necessary to differentiate the corresponding expression by time :
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The rate of decrease of the electromagnetic field energy in a closed volume.
The main relations between the characteristics of the electromagnetic field:
B curlE
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The rate of the field energy variation inside a closed volume :
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vE dV |
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The rate of decrease of the electromagnetic field energy in a closed volume.
Using the vector algebra formula : |
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we get: |
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After applying the Gauss theorem :
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Poynting 's Theorem.
The resulting expression is called the Poynting's theorem.
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The first term of this expression corresponds to energy losses for heating the conductor.
The second term is equal to the energy of the electric field spent on the acceleration of charged particles in the volume V.
The third term characterizes the energy of the electromagnetic fields carried across the boundaries of the area.
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The Poynting vector.
The power of radiated electromagnetic energy is numerically equal to the flow of energy through the surface per unit of time
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The Poynting vector :
E H S
The energy of the electromagnetic field is transmitted if the electric and magnetic field intensity vectors are not parallel
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Energy flows in the electromagnetic field
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Transmission of energy along the wires with current.
The energy transmitted along the wires of the line is propagated in the dielectric, as well as the energy emitted by the antenna. Wires and cables only serve as guides for this energy.
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An increase in the electromagnetic field energy stored inside the volume and the release of thermal energy in the line wires and in the load inside this volume can occur only due to the influx of electromagnetic field energy from the outside through the surface S, which limits this volume.
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Transmission of energy in a DC line.
All the energy entering the volume V through the surface s is released as heat in the receiver
E H ds1 E2 dV
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E H ds1 i2 R P
S
The energy of the electromagnetic field released in the conductors in the form of heat penetrates them through the surface of these conductors.
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sside. P i |
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Transmission of energy in a DC line.
Energy conversion in the elements of an electrical circuit.
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pR i2 R i uR
-Inductivity coil.
-Capacitor.
-Resistor
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Transmission of energy in a DC line.
Energy passing through the surface surrounding the load :
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dV i uL |
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i (uL uC uR ) i uab p |
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The power of the flow of electromagnetic energy entering the surface S is equal to the total power consumed in the circuit between ab terminals.
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