Lect_25_note

Lect_25_note - Chapter 32-3 Inductance Energy Density...

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Chapter 32-3 Inductance
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Energy Density ± Energy Density of Magnetic Field 2 2 B o UB u A μ == l ± Energy Density of Electric Field u E = ½ ε o E 2
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LC Circuit ± A capacitor is connected to an inductor ± Assume the capacitor is initially charged and then the switch is closed
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LC Circuit ± - Ld Ι / dt = V = Q/C ± Ι = dQ / dt ± d 2 Q / dt 2 = - Q/LC ± Q = Q max cos( ω t), = - Q max sin( t), 2 =1/LC
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Oscillations in an LC Circuit ± The charge on the capacitor oscillates between Q max and - Q max ± The current in the inductor oscillates between I max and - I max ± Q and I are 90 o out of phase with each other
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Energy in an LC Circuit ± The energy U L stored in the magnetic field of the inductor is U L = ½ L I 2 = ½ L Q max 2 ω 2 sin 2 ( t) ± Q = Q max cos( t), ± Ι = - Q max sin( t), 2 =1/LC
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Energy in an LC Circuit ± The energy continually oscillates between the energy stored in the electric and magnetic fields ± When the total energy is stored in one field, the energy stored in the other field is zero
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Energy in an LC Circuit ±
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This note was uploaded on 01/28/2011 for the course PHYS 011 taught by Professor Nianlin during the Fall '08 term at HKUST.

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Lect_25_note - Chapter 32-3 Inductance Energy Density...

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