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Resonance

ε and I in phase. i.e., load purely resistive. Resonance angular frequency:. Resonance. For given  peak , R , L , and C , the current amplitude I peak will be at the maximum when the impedance Z is at the minimum. This is called resonance. step-up step-down. Transformer.

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Resonance

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  1. ε and I in phase i.e., load purely resistive Resonance angular frequency: Resonance For given peak, R, L, and C, the current amplitude Ipeak will be at the maximum when the impedance Z is at the minimum. This is called resonance.

  2. step-up step-down Transformer • AC voltage can be stepped up or down by using a transformer. • AC current in the primary coil creates a time-varying magnetic flux through the secondary coil via the iron core. This induces EMF in the secondary circuit. Ideal transformer (no losses and magnetic flux per turn is the same on primary and secondary). (With no load) With resistive load R in secondary, current I2 flows in secondary by the induced EMF. This then induces opposing EMF back in the primary. The latter EMF must somehow be exactly cancelled because  is a defined voltage source. This occurs by another current I1 which is induced on the primary side due to I2.

  3. Gauss’s law Gauss’ law for magnetism Faraday’s law Ampere’s law* Maxwell’s Equations (so far)

  4. -Q Q will work. Parallel-Plate Capacitor Revisited

  5. is the displacement current. where Displacement Current James Clerk Maxwell proposed thata changing electric field induces a magnetic field,in analogy to Faraday’s law: A changing magnetic field induces an electric field. Ampere’s law is revised to become Ampere-Maxwell law

  6. Maxwell’s Equations Basis for electromagnetic waves!

  7. c Electromagnetic Waves From Faraday’s Law

  8. Electromagnetic Waves From Ampère’s Law

  9. So, again we have a traveling electromagnetic wave speed of light in vacuum Ampere’s Law Faraday’s Law Wave Equation Electromagnetic Wave Propagation in Free Space Speed of light in vacuum is currently defined rather than measured (thus defining meter and also the vacuum permittivity).

  10. where Plane Electromagnetic Waves • Transverse wave • Plane wave (points of given phase form a plane) • Linearly polarized (fixed plane contains E) x

  11. Non-scored Test Quiz Electromagnetic wave travel in space where E is electric field, B is magnetic field. Which of the following diagram is true? z z (a). (b). travel direction E E y y travel direction x B x B z travel direction z (c). (d). E E travel direction y y B x B x

  12. Electromagnetic waves contain energy. We know already expressions for the energy density stored in E and B fields: EM wave Energy Density of Electromagnetic Waves • SoTotal energy density is

  13. Energy flux density = Energy transmitted through unit time per unit area • Intensity I = Average energy flux density (W/m2) DefinePoynting vector • Direction is that of wave propagation • average magnitude is the intensity Energy Propagation in Electromagnetic Waves

  14. If radiation is totally absorbed: momentum imparted radiation pressure EXERTED • If radiation is totally reflected: Radiation Pressure Electromagnetic waves carry momentum as well as energy. In terms of total energy of a wave U, the momentum is U/c. During a time interval t , the energy flux through area A is U =IA t .

  15. Maxwell’s Rainbow Light is an Electromagnetic Wave

  16. Physics 241 –Quiz 18b – March 27, 2008 An electromagnetic wave is traveling through a particular point in space where the direction of the electric field is along the +z direction and that of the magnetic field is along +y direction at a certain instant in time. Which direction is this wave traveling in? • +x • x • y • z • None of the above

  17. Physics 241 –Quiz 18c – March 27, 2008 An electromagnetic wave is traveling in +y direction and the magnetic field at a particular point on the y-axis points in the +z direction at a certain instant in time. At this same point and instant, what is the direction of the electric field? • z • x • y • +x • None of the above

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