Chapter 24

1. Chapter 24 ELECTROMAGNETIC WAVES Electromagnetic waves ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES

2. ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES ELECTROMAGNETIC WAVES • So far you have learned • Coulomb’s Law – Ch. 19 • There are no Magnetic Monopoles – Ch. 22.1 • Faraday’s Law of Induction – Ch. 23 • Ampere’s Circuital Law – Ch. 22.9 Each law is empirical and Faraday’s is the most remarkable of these.

3. Faraday’s Law of Induction is: The EMF in a circuit is equal to the • Line integral of the magnetic field. • Surface integral of the curl of the magnetic field. • Rate of change of the magnetic flux enclosed by the circuit • Square of the hypotenuse of the current. • Inverse of the distance squared.

4. Faraday’s Law of Induction (Chapter 23) implies an electric field is produced by a changing magnetic field. Imagine a highly resistive loop of wire in a changing magnetic field…. Long solenoid with changing B . E B

5. Ampere’s circuital law (Chapter 22.9) is not correct for rapidly varying currents.

6. Something is rotten… Remember my “law”? Ampere Apply it to this case… For S1 : get I on the right But for S2: get zero on the right I is the current that crosses a surface bound by curve P

7. Something is rotten… Ampere

8. E Almost all electric flux goes through S2 Gauss’s law I can fix this! For S1 : get I on the right and No current goes through S2, but an electric field does!

9. E Gives dQ/dt across S1 Gives dQ/dt across S2 Take d/dt of this equation S2 S1

10. E I propose to replace I in Ampere’s law with: The Ampere-Maxwell Law: The ordinary electrical current The displacement current

11. Origin of the term “Displacement Current” Dielectric material -Q +Q I I The dielectric material is polarized by the displacement of bound charges, and there is a “displacement current” associated with the movement of the bound charges.

12. Origin of the term “Displacement Current” Vacuum -Q +Q I I The amazing experimental fact is that there is a “displacement current” associated with the [polarization of the] vacuum! The conclusion is that A magnetic field is produced by a changing electric field.

13. Direct observation of the “Displacement Current” is not so easy. In fact only conduction currents contribute to the magnetic field at low frequencies, so the first test by Hertz was really the best test of the Ampere-Maxwell law: the existence of Hertzian waves.

14. And the Lorentz force from E and B on A charges q: My equations: Gauss's law: electric flux~charge Magnetic Gauss's law: magnetic flux=0 Faraday's law: changing B generates an emf (Generalized) Ampere's law: Moving charges generate B

15. describe all electric and magnetic phenomena and LIGHT

16. Maxwell’s equations • May be derived from pure thought. • Are mathematical descriptions of empirical fact. • Are irrelevant to modern physics.

17. Electromagnetic waves If we look at Maxwell’s eqns where there are no charges or currents - after a bit of math we will get… 1) E and B are perpendicular 2) The Wave Equation Units of 1/speed2

18. Suppose we start with a sine wave electric field in the x direction traveling in the z direction: The Ampere-Maxwell law says

19. Then the Faraday law of induction says This can only be true if

20. Units of 1/speed2 The speed of the waves is the speed of light • Light is an electromagentic wave • It is described by Maxwell’s equations • Electricity, magnetism and optics are different aspects of the same theory

21. This is in the vacuum. In a medium of dielectric constant eand magnetic permeability m the speed of light is the speed of light in vacuum is the largest speed...period!