2. Physics 1202: Lecture 18 Today’s Agenda Announcements: –Lectures posted on: www.phys.uconn.edu/~rcote/ www.phys.uconn.edu/~rcote/ –HW assignments, etc. Homework #5:Homework #5: –Due this Friday

3. f()x x f(x x z y

4. Generating E-M Waves Static charges produce a constant Electric Field but no Magnetic Field. Moving charges (currents) produce both a possibly changing electric field and a static magnetic field. Accelerated charges produce EM radiation (oscillating electric and magnetic fields). Antennas are often used to produce EM waves in a controlled manner.

5. A Dipole Antenna V(t)=V o cos(  t) x z y time t=0 ++++ ---- E time t=  /2  E time t=  /  one half cycle later ---- ++++

6. dipole radiation pattern oscillating electric dipole generates e-m radiation that is polarized in the direction of the dipole radiation pattern is doughnut shaped & outward traveling –zero amplitude directly above and below dipole –maximum amplitude in-plane proportional to sin(  t)

7. Receiving E-M Radiation receiving antenna One way to receive an EM signal is to use the same sort of antenna. Receiving antenna has charges which are accelerated by the E field of the EM wave. The acceleration of charges is the same thing as an EMF. Thus a voltage signal is created. Speaker y x z

8. Lecture 18, ACT 1 Consider an EM wave with the E field POLARIZED to lie perpendicular to the ground. y x z In which orientation should you turn your receiving dipole antenna in order to best receive this signal? C) Along E a) Along S b) Along B

9. Loop Antennas Magnetic Dipole Antennas The electric dipole antenna makes use of the basic electric force on a charged particle Note that you can calculate the related magnetic field using Ampere’s Law. We can also make an antenna that produces magnetic fields that look like a magnetic dipole, i.e. a loop of wire. This loop can receive signals by exploiting Faraday’s Law. For a changing B field through a fixed loop of area A:   = A B

10. Lecture 18, ACT 2 Consider an EM wave with the E field POLARIZED to lie perpendicular to the ground. y x z In which orientation should you turn your receiving loop antenna in order to best receive this signal? a) â Along S b) â Along B C) â Along E

11. Review of Waves from 1201 The one-dimensional wave equation: A specific solution for harmonic waves traveling in the +x direction is: has a general solution of the form: where h 1 represents a wave traveling in the +x direction and h 2 represents a wave traveling in the -x direction. h x A A = amplitude = wavelength f = frequency v = speed k = wave number

12. E & B in Electromagnetic Wave Plane Harmonic Wave: where: y x z From general properties of waves : 

13. Velocity of Electromagnetic Waves The wave equation for E x : (derived from Maxwell’s Eqn) Therefore, we now know the velocity of electromagnetic waves in free space: Putting in the measured values for  0 &  0, we get: This value is identical to the measured speed of light! –We identify light as an electromagnetic wave.

14. The EM Spectrum These EM waves can take on any wavelength from angstroms to miles (and beyond). We give these waves different names depending on the wavelength. Wavelength [m] 10 -14 10 -10 10 -6 10 -2 110 2 10 6 10 10 Gamma Rays Infrared Microwaves Short Wave Radio TV and FM Radio AM Radio Long Radio Waves Ultraviolet Visible Light X Rays

15. Lecture 18, ACT 3 Consider your favorite radio station. I will assume that it is at 100 on your FM dial. That means that it transmits radio waves with a frequency f=100 MHz. What is the wavelength of the signal ? A) 3 cmB) 3 mC) ~0.5 mD) ~500 m

16. The EM Spectrum Each wavelength shows different details

17. The EM Spectrum Each wavelength shows different details

18. Energy in EM Waves / review Electromagnetic waves contain energy which is stored in E and B fields: The Intensity of a wave is defined as the average power transmitted per unit area = average energy density times wave velocity: Therefore, the total energy density in an e-m wave = u, where =

19. Momentum in EM Waves Electromagnetic waves contain momentum: We use the above expression plus Newton’s Second Law in the form F=  p/  t to derive the following expression for the Pressure,  momentum transferred If a surface completely absorbs the incident light, the momentum gained by the surface p The momentum transferred to a surface depends on the area of the surface. Thus Pressure is a more useful quantity.

20. Momentum in EM Waves  If the surface completely reflects the light, conservation of momentum indicates the light pressure will be double that for the surface that absorbs. Idea for spaceship engine: solar sail !

22. Constant speed of light In late 1800, speed of light measured to within 1% “usual” waves propagate in a medium –Sound in air/liquid/solid –Surf in water What about light (electromagnetic wave) ? –must require a medium: luminiferous ether or simply “ether” To try to detect it: Michelson-Morley experiment –1881 and 1887 –Interferometer: c+v ? c v Sun

23. Constant speed of light Michelson-Morley experiment: –2 paths of same length –1 perp. To direction of “ether” –1 // to direction of “ether” If v of light varies –Interference pattern None detected with any orientation c is constant No evidence of ether !

24. Einstein’s relativity Einstein incorporated this result in his 2 postulates 2- Constant speed of light: The speed of light c is the same in all inertial reference frames, regardless of the relative velocity of the source and receiver of the light. 1- Principle of Relativity: The laws of Physics are the same on all inertial reference frame. These “simple” postulates have big implications …