Chapter 24 Electromagnetic waves

So far you have learned 1.Coulomb’s Law – Ch There are no Magnetic Monopoles – Ch Faraday’s Law of Induction – Ch Ampere’s Circuital Law – Ch Each law is empirical and Faraday’s is the most remarkable of these.

Faraday’s Law of Induction is: The EMF in a circuit is equal to the 1.Line integral of the magnetic field. 2.Surface integral of the curl of the magnetic field. 3.Rate of change of the magnetic flux enclosed by the circuit 4.Square of the hypotenuse of the current. 5.Inverse of the distance squared.

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

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

Something is rotten… Remember my “law”? For S 1 : get I on the right But for S 2 : get zero on the right Apply it to this case… I is the current that crosses a surface bound by curve P

Something is rotten…

I can fix this! No current goes through S 2, but an electric field does! For S 1 : get I on the right and E Gauss’s law Almost all electric flux goes through S 2

E Take d/dt of this equation Gives dQ/dt across S 1 Gives dQ/dt across S 2 S1S1 S2S2

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

Origin of the term “Displacement Current” Dielectric material -Q+Q II 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.

Origin of the term “Displacement Current” Vacuum -Q+Q II 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.

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.

My equations: And the Lorentz force from E and B on A charges q:

describe all electric and magnetic phenomena and LIGHT

Maxwell’s equations 1.May be derived from pure thought. 2.Are mathematical descriptions of empirical fact. 3.Are irrelevant to modern physics.

Electromagnetic waves If we look at Maxwell’s eqns where there are no charges or currents - after a bit of math we will get… Units of 1/speed 2

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

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

The speed of the waves is Units of 1/speed 2 Light is an electromagentic wave It is described by Maxwell’s equations Electricity, magnetism and optics are different aspects of the same theory

This is in the vacuum. In a medium of dielectric constant  and magnetic permeability  the speed of light is