Page 1 Poynting’s Theorem Poynting’s Theorem … energy conservation … energy conservation John Henry Poynting (1852-1914) Page 2 Poynting’s Theorem Poynting’s Theorem … energy conservation … energy conservation John Henry Poynting (1852-1914) To recap… To recap… nn The energy stored in an electric field E is The energy stored in an electric field E is expressed as the work needed to “assemble” a expressed as the work needed to “assemble” a group of point charges group of point charges 2 1 2 2 1 2 Eo Eo uE W E dV e e = = ò Page 3 Poynting’s Theorem Poynting’s Theorem … energy conservation … energy conservation John Henry Poynting (1852-1914) To recap… To recap… nn The energy stored in an electric field E is The energy stored in an electric field E is expressed as the work needed to “assemble” a expressed as the work needed to “assemble” a group of point charges group of point charges 2 1 2 2 1 2 Eo Eo uE W E dV e e = = ò nn Magnetic fields also store energy Magnetic fields also store energy nn Total energy stored by electromagnetic fields per unit Total energy stored by electromagnetic fields per unit volume is… volume is… 2 1 2 2 1 2 o o B B uB W B dV m m = = ò 22 11 () 2 o o u EB e m =+ Page 4 Poynting’s Theorem Poynting’s Theorem … energy conservation … energy conservation John Henry Poynting (1852-1914) To recap… To recap… nn The energy stored in an electric field E is The energy stored in an electric field E is expressed as the work needed to “assemble” a expressed as the work needed to “assemble” a group of point charges group of point charges 2 1 2 2 1 2 Eo Eo uE W E dV e e = = ò nn Magnetic fields also store energy Magnetic fields also store energy nn Total energy stored by electromagnetic fields per unit Total energy stored by electromagnetic fields per unit volume is… volume is… 2 1 2 2 1 2 o o B B uB W B dV m m = = ò 22 11 () 2 o o u EB e m =+ Work done moving a charge… Work done moving a charge… nn Use the Lorentz formula: Use the Lorentz formula: nn The work in time The work in time- -interval dt is then: interval dt is then: () F qE vB = +´ () dW F dl q E v B dl qE vdt = ×= + ´ ×= × (remember: Magnetic fields do no work!) Page 5 Poynting’s Theorem Poynting’s Theorem … energy conservation … energy conservation John Henry Poynting (1852-1914) To recap… To recap… nn The energy stored in an electric field E is The energy stored in an electric field E is expressed as the work needed to “assemble” a expressed as the work needed to “assemble” a group of point charges group of point charges 2 1 2 2 1 2 Eo Eo uE W E dV e e = = ò nn Magnetic fields also store energy Magnetic fields also store energy nn Total energy stored by electromagnetic fields per unit Total energy stored by electromagnetic fields per unit volume is… volume is… 2 1 2 2 1 2 o o B B uB W B dV m m = = ò 22 11 () 2 o o u EB e m =+ Work done moving a charge… Work done moving a charge… nn Use the Lorentz formula: Use the Lorentz formula: nn The work in time The work in time- -interval dt is then: interval dt is then: () F qE vB = +´ () dW F dl q E v B dl qE vdt = ×= + ´ ×= × (remember: Magnetic fields do no work!) nn Remember current density J! The moving Remember current density J! The moving charge or charges constitute a current charge or charges constitute a current density, so we can write density, so we can write which means the work can now be which means the work can now be expressed as expressed as qE vdt E J × =× () dW E J dV dt =× ò Remember that this is a rate of change of the energy (work) and so represents power delivered per unit volumeRead More

29 videos|49 docs|70 tests

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### Test: Maxwell Law In Time Static Fields

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### Test: Maxwell Law In Time Varying Fields

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### Conservation of Energy and Momentum (Part - 2)

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