Electromagnetic Waves

Transcription

1 Eletroagneti Waves Physis 6C

2 Eletroagneti (EM) waves an be produed by atoi transitions (ore on this later), or by an alternating urrent in a wire. As the harges in the wire osillate bak and forth, the eletri field around the osillates as well, in turn produing an osillating agneti field. This agneti field is always perpendiular to the eletri field, and the EM wave propagates perpendiular to both the E- and B-fields. This gives us a right-hand-rule relating the diretions of these 3 vetors: 1) Point the fingers of your right hand in the diretion of the E-field ) Curl the toward the B-field. Eletroagneti Waves 3) Stik out your thub - it points in the diretion of propagation. Clik here for an EM wave aniation

3 Like any other wave, we know the relationship between the wavelength and frequeny, and the speed of propagation of the wave: v wave f

4 Like any other wave, we know the relationship between the wavelength and frequeny, and the speed of propagation of the wave: v wave f In the ase of EM waves, it turns out that the wave speed is the speed of light. So our forula for EM waves (in vauu) is: f 1 ; s

5 Like any other wave, we know the relationship between the wavelength and frequeny, and the speed of propagation of the wave: v wave f In the ase of EM waves, it turns out that the wave speed is the speed of light. So our forula for EM waves (in vauu) is: f 1 ; s It turns out that the speed of light is also related to the strengths of the Eletri and Magneti fields. E=B (in standard etri units)

6 Like any other wave, we know the relationship between the wavelength and frequeny, and the speed of propagation of the wave: v wave f In the ase of EM waves, it turns out that the wave speed is the speed of light. So our forula for EM waves (in vauu) is: f 1 ; s It turns out that the speed of light is also related to the strengths of the Eletri and Magneti fields. E=B (in standard etri units) The ontinuu of various wavelengths and frequenies for EM waves is alled the Eletroagneti Spetru

7 Exaples: Find the frequeny of blue light with a wavelength of 46 n.

8 Exaples: Find the frequeny of blue light with a wavelength of 46 n. f f s Hz

9 Exaples: Find the frequeny of blue light with a wavelength of 46 n. f f s Hz A ell phone transits at a frequeny of 1.5x1 8 Hz. What is the wavelength of this EM wave?

10 Exaples: Find the frequeny of blue light with a wavelength of 46 n. f f s Hz A ell phone transits at a frequeny of 1.5x1 8 Hz. What is the wavelength of this EM wave? f f s Hz.4 You will need to use this forula very often to onvert bak and forth between frequeny and wavelength.

11 Energy and oentu in EM Waves Eletroagneti waves transport energy. The energy assoiated with a wave is stored in the osillating eletri and agneti fields. We will find out later that the frequeny of the wave deterines the aount of energy that it arries. Sine the EM wave is in 3-D, we need to easure the energy density (energy per unit volue). u avg 1 E E rs B 1 1 rs B This is the energy per unit volue Note that the energy an be written in a few equivalent fors. Eah an be useful, depending on the inforation you know about the wave.

12 Energy and oentu in EM Waves Eletroagneti waves transport energy. The energy assoiated with a wave is stored in the osillating eletri and agneti fields. We will find out later that the frequeny of the wave deterines the aount of energy that it arries. Sine the EM wave is in 3-D, we need to easure the energy density (energy per unit volue). u avg 1 E E rs B 1 1 rs B This is the energy per unit volue Note that the energy an be written in a few equivalent fors. Eah an be useful, depending on the inforation you know about the wave. We an also talk about the intensity of an EM wave (for light we would think of it as brightness). Just as for sound, intensity is easured as average power/area. S Power Area avg u avg Just ultiply the energy equation above by the speed of light to get the intensity.

13 Exaple: High-Energy Caner Treatent Sientists are working on a tehnique to kill aner ells by zapping the with ultrahighenergy pulses of light that last for an extreely short aount of tie. These short pulses srable the interior of a ell without ausing it to explode, as long pulses do. We an odel a typial suh ell as a disk 5. µ in diaeter, with the pulse lasting for 4. ns with an average power of.x1 1 W. We shall assue that the energy is spread uniforly over the faes of 1 ells for eah pulse. a) How uh energy is given to the ell during this pulse? b) What is the intensity (in W/ ) delivered to the ell? ) What are the axiu values of the eletri and agneti fields in the pulse?

14 Exaple: High-Energy Caner Treatent Sientists are working on a tehnique to kill aner ells by zapping the with ultrahighenergy pulses of light that last for an extreely short aount of tie. These short pulses srable the interior of a ell without ausing it to explode, as long pulses do. We an odel a typial suh ell as a disk 5. µ in diaeter, with the pulse lasting for 4. ns with an average power of.x1 1 W. We shall assue that the energy is spread uniforly over the faes of 1 ells for eah pulse. a) How uh energy is given to the ell during this pulse? b) What is the intensity (in W/ ) delivered to the ell? ) What are the axiu values of the eletri and agneti fields in the pulse? Reall that power is energy/tie. So.x1 1 W is.x1 1 Joules/se. Energy (. 1 1 J s ) ( s) J 8J This is the total energy, whih is spread out over 1 ells, so the energy for eah individual ell is 8 Joules.

15 Exaple: High-Energy Caner Treatent Sientists are working on a tehnique to kill aner ells by zapping the with ultrahighenergy pulses of light that last for an extreely short aount of tie. These short pulses srable the interior of a ell without ausing it to explode, as long pulses do. We an odel a typial suh ell as a disk 5. µ in diaeter, with the pulse lasting for 4. ns with an average power of.x1 1 W. We shall assue that the energy is spread uniforly over the faes of 1 ells for eah pulse. a) How uh energy is given to the ell during this pulse? b) What is the intensity (in W/ ) delivered to the ell? ) What are the axiu values of the eletri and agneti fields in the pulse? To get intensity, we need to divide power/area. The area for a ell is just the area of a irle: Area r ( ). 1 11

16 Exaple: High-Energy Caner Treatent Sientists are working on a tehnique to kill aner ells by zapping the with ultrahighenergy pulses of light that last for an extreely short aount of tie. These short pulses srable the interior of a ell without ausing it to explode, as long pulses do. We an odel a typial suh ell as a disk 5. µ in diaeter, with the pulse lasting for 4. ns with an average power of.x1 1 W. We shall assue that the energy is spread uniforly over the faes of 1 ells for eah pulse. a) How uh energy is given to the ell during this pulse? b) What is the intensity (in W/ ) delivered to the ell? ) What are the axiu values of the eletri and agneti fields in the pulse? To get intensity, we need to divide power/area. The area for a ell is just the area of a irle: Area r ( ) Now divide to get intensity: Intensity Power 1 r W W This is the total area of all 1 ells.

17 Exaple: High-Energy Caner Treatent Sientists are working on a tehnique to kill aner ells by zapping the with ultrahighenergy pulses of light that last for an extreely short aount of tie. These short pulses srable the interior of a ell without ausing it to explode, as long pulses do. We an odel a typial suh ell as a disk 5. µ in diaeter, with the pulse lasting for 4. ns with an average power of.x1 1 W. We shall assue that the energy is spread uniforly over the faes of 1 ells for eah pulse. a) How uh energy is given to the ell during this pulse? b) What is the intensity (in W/ ) delivered to the ell? ) What are the axiu values of the eletri and agneti fields in the pulse? To get the field strengths, reall our forulas: u avg 1 E E rs B B 1 1 rs S avg Power Area u avg

18 Exaple: High-Energy Caner Treatent Sientists are working on a tehnique to kill aner ells by zapping the with ultrahighenergy pulses of light that last for an extreely short aount of tie. These short pulses srable the interior of a ell without ausing it to explode, as long pulses do. We an odel a typial suh ell as a disk 5. µ in diaeter, with the pulse lasting for 4. ns with an average power of.x1 1 W. We shall assue that the energy is spread uniforly over the faes of 1 ells for eah pulse. a) How uh energy is given to the ell during this pulse? b) What is the intensity (in W/ ) delivered to the ell? ) What are the axiu values of the eletri and agneti fields in the pulse? To get the field strengths, reall our forulas: u avg 1 E E rs B B 1 1 rs S avg Power Area u avg Sine the power was stated as average power we should assue that is the rs value. So our field values should get ultiplied by to find the axiu. S E S B V T

19 Photons The energy arried by an EM wave oes in pakets alled photons. The energy of a photon depends on the frequeny of the EM wave. E photon hf The onstant h is alled Plank s onstant. Notie that this is an inredibly sall nuber. h 6.66 x 1 34 J s

20 Photons The energy arried by an EM wave oes in pakets alled photons. The energy of a photon depends on the frequeny of the EM wave. E photon hf The onstant h is alled Plank s onstant. Notie that this is an inredibly sall nuber. h h 6.66 x 1 34 J s Beause photon energies are usually so sall, it is often onvenient to express their energy in units of eletron-volts (ev) instead of Joules. Reall the onversion fator: 1 ev = 1.6x1-19 J

21 Photons The energy arried by an EM wave oes in pakets alled photons. The energy of a photon depends on the frequeny of the EM wave. E photon hf The onstant h is alled Plank s onstant. h Notie that this is an inredibly sall nuber. h 6.66 x 1 34 J s Beause photon energies are usually so sall, it is often onvenient to express their energy in units of eletron-volts (ev) instead of Joules. Reall the onversion fator: 1 ev = 1.6x1-19 J For onveniene, Plank s onstant an be onverted to ev instead of Joules: h 4.14 x 1 15 ev s This will be useful when dealing with photon energies.

22 Photons Exaple: A typial x-ray ahine sans the body with EM waves of frequeny 7x1 18 Hz. How uh energy is in a typial x-ray photon?

23 Photons Exaple: A typial x-ray ahine sans the body with EM waves of frequeny 7x1 18 Hz. How uh energy is in a typial x-ray photon? We an give the answer in Joules or ev: E photon hf E photon ( J s)(7 1 Hz) E photon ( ev s)(7 1 Hz) 9,eV 9keV J

24 Energy and oentu in EM Waves EM waves also arry oentu. This eans that a ray of light an atually exert a fore. To get the pressure exerted by a sinusoidal EM wave, just divide the intensity by the speed of light. Radiation Pr essure S avg This is the sae as the total energy absorbed by the surfae.

25 Energy and oentu in EM Waves EM waves also arry oentu. This eans that a ray of light an atually exert a fore. To get the pressure exerted by a sinusoidal EM wave, just divide the intensity by the speed of light. Radiation Pr essure S avg Exaple: Solar Sails Suppose a spaeraft with a ass of 5, kg has a solar sail ade of perfetly refletive aluinized fil with an area of.59x1 6. If the spaeraft is launhed into earth orbit and then deploys its sail at right angles to the sunlight, what is the aeleration due to sunlight? Assue that at the earth s distane fro the sun, the pressure exerted by sunlight on an absorbing surfae is 4.7x1-6 Pa.

26 Exaple: Solar Sails Suppose a spaeraft with a ass of 5, kg has a solar sail ade of perfetly refletive aluinized fil with an area of.59x1 6. If the spaeraft is launhed into earth orbit and then deploys its sail at right angles to the sunlight, what is the aeleration due to sunlight? Assue that at the earth s distane fro the sun, the pressure exerted by sunlight on an absorbing surfae is 4.7x1-6 Pa. Reall that Pressure = Fore/Area. We an use this and F=a to get our forula: P F F A a F P A a F a P A Now for the triky part: When the pressure nuber was given above, that was for an absorbing surfae. What happens when the sunlight reflets instead?

27 Exaple: Solar Sails Suppose a spaeraft with a ass of 5, kg has a solar sail ade of perfetly refletive aluinized fil with an area of.59x1 6. If the spaeraft is launhed into earth orbit and then deploys its sail at right angles to the sunlight, what is the aeleration due to sunlight? Assue that at the earth s distane fro the sun, the pressure exerted by sunlight on an absorbing surfae is 4.7x1-6 Pa. Reall that Pressure = Fore/Area. We an use this and F=a to get our forula: P F F A a F P A a F a P A Now for the triky part: When the pressure nuber was given above, that was for an absorbing surfae. What happens when the sunlight reflets instead? Twie as uh oentu is transferred! a ( N.5 1 ) kg s