1. Lecture 21-1 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. Resonance angular frequency: This is called resonance. i.e., load purely resistiveε and I in phase

2. Lecture 21-2 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) step-up step-down With resistive load R in secondary, current I 2 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 I 1 which is induced on the primary side due to I 2.

3. Lecture 21-3 Maxwell’s Equations (so far) Gauss’s law Gauss’ law for magnetism Faraday’s lawAmpere’s law *

4. Lecture 21-4 Parallel-Plate Capacitor Revisited will work. Q -Q

5. Lecture 21-5 Displacement Current James Clerk Maxwell proposed that a 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 is the displacement current. where

6. Lecture 21-6 Maxwell’s Equations Basis for electromagnetic waves!

7. Lecture 21-7 Electromagnetic Waves From Faraday’s Law c

8. Lecture 21-8 Electromagnetic Waves From Ampère’s Law

9. Lecture 21-9 Electromagnetic Wave Propagation in Free Space So, again we have a traveling electromagnetic wave speed of light in vacuum Speed of light in vacuum is currently defined rather than measured (thus defining meter and also the vacuum permittivity). Ampere’s Law Faraday’s Law Wave Equation

10. Lecture 21-10 Plane Electromagnetic Waves where x Transverse wave Plane wave (points of given phase form a plane) Linearly polarized (fixed plane contains E)

11. Lecture 21-11 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 x y travel direction B E z x y B E z x y B E z x y B E (a). (d). (b). (c).

12. Lecture 21-12 Energy Density of Electromagnetic Waves Electromagnetic waves contain energy. We know already expressions for the energy density stored in E and B fields: EM wave So Total energy density is

13. Lecture 21-13 Energy Propagation in Electromagnetic Waves Energy flux density = Energy transmitted through unit time per unit area Intensity I= Average energy flux density (W/m 2 ) Define Poynting vector  Direction is that of wave propagation  average magnitude is the intensity

14. Lecture 21-14 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. momentum imparted radiation pressure EXERTED  If radiation is totally absorbed:  If radiation is totally reflected:

15. Lecture 21-15 Maxwell’s Rainbow Light is an Electromagnetic Wave

16. Lecture 21-16 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? a)+x b)  x c)  y d)  z e)None of the above

17. Lecture 21-17 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? a)  z b)  x c)  y d)+x e)None of the above