Chapter 34 Electromagnetic Waves

1. Chapter 34 Electromagnetic Waves

2. Chapter 34: Electromagnetic Waves

3. Chapter Outline • 1. Changing Electric Fields • Produce Magnetic Fields • 2. Modification of Ampère’s Law • Maxwell’s Displacement Current • 3. Gauss’s Law for Magnetism • Production of Electromagnetic Waves • Electromagnetic Waves, & Their Speed Maxwell’s Equations

4. Derived from Maxwell’s Equations: • Light as an Electromagnetic Wave • The Electromagnetic Spectrum • Measuring the Speed of Light • Energy in Electromagnetic Waves • The Poynting Vector • Radiation Pressure • Radio & Television • Wireless Communication

5. Changing Electric Fields Produce Magnetic Fields: Ampère’s Law& Displacement CurrentMaxwell’s Generalization of Ampère’s Law RecallCh. 30 Ampère’s Law: Consider a wire carrying a Current I Relates the magnetic field B around a current to the current Ienclthrough a surface. Also Ch. 30:The Magnetic Fluxthrough a surface is definedas

6. Changing Electric Fields Produce Magnetic Fields: Ampère’s Law& Displacement CurrentMaxwell’s Generalization of Ampère’s Law Ch. 31:Faraday’s Law: “Theemf inducedin a circuit is equal to the timerate of changeof magnetic flux through the circuit.” So, changing Magnetic Fieldsproduce currents & thus Electric Fields.

7. Maxwell’s reasoning about Ampère’s Law:In order it to hold, it can’t matter which surface is chosen. But look at a discharging capacitor; there is a current through surface 1 but none through surface 2: Therefore,Maxwell modified Ampère’s Law to include the creation of a magnetic field by a changing electric field.Analogous to Faraday’s Law which says that electric fields can be produced by changing magnetic fields. In the case shown, the electric field between the plates of the capacitor is changing & so:

8. Example: Charging capacitor. A 30-pF air-gap capacitor has circular plates of area A = 100 cm2. It is charged by a 70-V battery through a 2.0-Ωresistor. At the instant the battery is connected, the electric field between the plates is changing most rapidly. At this instant, calculate (a) the current into the plates, and (b) the rate of change of electric field between the plates. (c) Determine the magnetic field induced between the plates. Assume E is uniform between the plates at any instant and is zero at all points beyond the edges of the plates.

9. The second term in Ampere’s Law, first written by Maxwell, has the dimensions of a current (after factoring out the μ0), and is sometimes called the displacement current: where

10. Gauss’s Law for Magnetism Gauss’s law relates the electric field on a closed surface to the net charge enclosed by that surface. The analogous law for magnetic fields is different, as there are no single magnetic point charges (monopoles):

11. Maxwell’s Equations We now have a complete set of equations that describe electric and magnetic fields, called Maxwell’s Equations. In the absence of dielectric or magnetic materials, they are:

12. Production of Electromagnetic Waves Since a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field, once sinusoidal fields are created, they can propagate on their own. These propagating fields are called electromagnetic waves.

13. Close to the antenna, the fields are complicated, and are called the near field: Oscillating charges will produce electromagnetic waves:

14. Far from the source, the waves are plane waves:

15. The electric and magnetic waves are perpendicular to each other, and to the direction of propagation.