1. Physics for Scientists and Engineers II, Summer Semester 2009 1 Lecture 21: July 13 th 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 2 Plane Electromagnetic Waves Plane linearly polarized electromagnetic waves with propagation in x-direction. y z x Properties: 1)Wherever in the yz plane em wave comes from, it propagates in the x-direction. (all “rays” of this wave are parallel). 2) All em waves coming from different parts of the yz plane are all in phase. 3) Electric and magnetic waves oscillate perpendicular to each other (take this by faith for now). 4) Electric field is in the same direction (here in y-direction)  “linearly polarized”. 5) Magnetic field is in the same direction (here in z-direction)  “linearly polarized”. 6) And B are only function of x and t and do not depend on y and z  E(x,t), B(x,t). E B

3. Physics for Scientists and Engineers II, Summer Semester 2009 3 Let’s check such a wave for consistency with Maxwell’s equations: y z x

4. Physics for Scientists and Engineers II, Summer Semester 2009 4 …….. consistency with Maxwell’s equations: y z x

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 …….. consistency with Maxwell’s equations:

6. Physics for Scientists and Engineers II, Summer Semester 2009 6 …….. consistency with Maxwell’s equations:

7. Physics for Scientists and Engineers II, Summer Semester 2009 7 Let’s check such a wave for consistency with Maxwell’s equations: Note: These diff. equations are linear equations  We can use the principle of superposition (adding different waves) of solutions.

8. Physics for Scientists and Engineers II, Summer Semester 2009 8 Energy Carried by Electromagnetic Waves z x E B “unit surface area” perpendicular to the pointing vector.

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Poynting Vector for Plane Electromagnetic Wave Instantaneous rate at which energy passes through the unit surface area. Of more interest: The time average of S over one or more cycles of the wave. This time average is called wave intensity I.

10. Physics for Scientists and Engineers II, Summer Semester 2009 10 Energy Density of Electromagnetic Radiation

11. Physics for Scientists and Engineers II, Summer Semester 2009 11 Example: Problem 16 An AM radio station broadcasts isotropically (equally in all directions) with an average power of 4.00 KW. A dipole receiving antenna 65.0 cm long is at a location 4.00 miles from the transmitter. Compute the amplitude of the emf induced by this signal between the ends of the receiving antenna.