1. Copyright © 2009 Pearson Education, Inc. Chapter 34 Electromagnetic Waves

2. Copyright © 2009 Pearson Education, Inc. Chapter 34: Electromagnetic Waves

3. Copyright © 2009 Pearson Education, Inc. 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 Chapter Outline Maxwell’s Equations

4. Copyright © 2009 Pearson Education, Inc. Derived from Maxwell’s Equations: 1. Light as an Electromagnetic Wave 2. The Electromagnetic Spectrum 3. Measuring the Speed of Light 4. Energy in Electromagnetic Waves The Poynting Vector Radiation Pressure Radio & Television Wireless Communication

5. Copyright © 2009 Pearson Education, Inc. Changing Electric Fields Produce Magnetic Fields: Ampère’s Law & Displacement Current Maxwell’s Generalization of Ampère’s Law Also Ch. 30: The Magnetic Flux through a surface is defined as Relates the magnetic field B around a current to the current I encl through a surface. Recall Ch. 30 Ampère’s Law: Consider a wire carrying a Current I

6. Copyright © 2009 Pearson Education, Inc. Ch. 31: Faraday’s Law: “The emf induced in a circuit is equal to the time rate of change of magnetic flux through the circuit.” Changing Electric Fields Produce Magnetic Fields: Ampère’s Law & Displacement Current Maxwell’s Generalization of Ampère’s Law So, changing Magnetic Fields produce currents & thus Electric Fields.

7. Copyright © 2009 Pearson Education, Inc. 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: 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:

8. Copyright © 2009 Pearson Education, Inc. Example: Charging capacitor. A 30-pF air-gap capacitor has circular plates of area A = 100 cm 2. It is charged by a 70-V battery through a 2.0-Ω resistor. 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. Copyright © 2009 Pearson Education, Inc. The second term in Ampere’s Law, first written by Maxwell, has the dimensions of a current (after factoring out the μ 0 ), and is sometimes called the displacement current: where

10. Copyright © 2009 Pearson Education, Inc. 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. Copyright © 2009 Pearson Education, Inc. 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. Copyright © 2009 Pearson Education, Inc. 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. Production of Electromagnetic Waves

13. Copyright © 2009 Pearson Education, Inc. Oscillating charges will produce electromagnetic waves: Close to the antenna, the fields are complicated, and are called the near field:

14. Copyright © 2009 Pearson Education, Inc. Far from the source, the waves are plane waves:

15. Copyright © 2009 Pearson Education, Inc. The electric and magnetic waves are perpendicular to each other, and to the direction of propagation.