# Electromagnetic Waves Physics 6C Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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Electromagnetic Waves Physics 6C Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 2 Electromagnetic (EM) waves are produced by an alternating current in a wire. As the charges in the wire oscillate back and forth, the electric field around them oscillates as well, in turn producing an oscillating magnetic field. This magnetic field is always perpendicular to the electric field, and the EM wave propagates perpendicular to both the E- and B-fields. This gives us a right-hand-rule relating the directions of these 3 vectors: 1) Point the fingers of your right hand in the direction of the E-field 2) Curl them toward the B-field. 3) Stick out your thumb - it points in the direction of propagation. Electromagnetic Waves Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Click here for an EM wave animation Slide 3 Like any other wave, we know the relationship between the wavelength and frequency, and the speed of propagation of the wave: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 4 Like any other wave, we know the relationship between the wavelength and frequency, and the speed of propagation of the wave: In the case of EM waves, it turns out that the wave speed is the speed of light. So our formula for EM waves (in vacuum) is: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 5 Like any other wave, we know the relationship between the wavelength and frequency, and the speed of propagation of the wave: In the case of EM waves, it turns out that the wave speed is the speed of light. So our formula for EM waves (in vacuum) is: It turns out that the speed of light is also the ratio of the strengths of the Electric and Magnetic fields in an EM wave. So we know that E=cB (in standard metric units) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 6 Like any other wave, we know the relationship between the wavelength and frequency, and the speed of propagation of the wave: In the case of EM waves, it turns out that the wave speed is the speed of light. So our formula for EM waves (in vacuum) is: The continuum of various wavelengths and frequencies for EM waves is called the Electromagnetic Spectrum It turns out that the speed of light is also the ratio of the strengths of the Electric and Magnetic fields in an EM wave. So we know that E=cB (in standard metric units) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 7 Examples: Find the frequency of blue light with a wavelength of 460 nm. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 8 Examples: Find the frequency of blue light with a wavelength of 460 nm. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 9 Examples: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Find the frequency of blue light with a wavelength of 460 nm. A cell phone transmits at a frequency of 1.25x10 8 Hz. What is the wavelength of this EM wave? Slide 10 Examples: Find the frequency of blue light with a wavelength of 460 nm. A cell phone transmits at a frequency of 1.25x10 8 Hz. What is the wavelength of this EM wave? You will need to use this formula very often to convert back and forth between frequency and wavelength. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 11 Energy and momentum in EM Waves Electromagnetic waves transport energy. The energy associated with a wave is stored in the oscillating electric and magnetic fields. We will find out later that the frequency of the wave determines the amount of energy that it carries. Since the EM wave is in 3-D, we need to measure the energy density (energy per unit volume). Note that the energy can be written in a few equivalent forms. Each can be useful, depending on the information you know about the wave. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 12 Energy and momentum in EM Waves Electromagnetic waves transport energy. The energy associated with a wave is stored in the oscillating electric and magnetic fields. We will find out later that the frequency of the wave determines the amount of energy that it carries. Since the EM wave is in 3-D, we need to measure the energy density (energy per unit volume). Note that the energy can be written in a few equivalent forms. Each can be useful, depending on the information you know about the wave. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB We can also talk about the intensity of an EM wave (for light we would think of it as brightness). Just as for sound, intensity is measured as average power/area. Just multiply the energy equation above by the speed of light to get the intensity. This is the energy per unit volume Slide 13 Example: High-Energy Cancer Treatment Scientists are working on a technique to kill cancer cells by zapping them with ultrahigh- energy pulses of light that last for an extremely short amount of time. These short pulses scramble the interior of a cell without causing it to explode, as long pulses do. We can model a typical such cell as a disk 5.0 m in diameter, with the pulse lasting for 4.0 ns with an average power of 2.0x10 12 W. We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse. a) How much energy is given to the cell during this pulse? b) What is the intensity (in W/m 2 ) delivered to the cell? c) What are the maximum values of the electric and magnetic fields in the pulse? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 14 Example: High-Energy Cancer Treatment Scientists are working on a technique to kill cancer cells by zapping them with ultrahigh- energy pulses of light that last for an extremely short amount of time. These short pulses scramble the interior of a cell without causing it to explode, as long pulses do. We can model a typical such cell as a disk 5.0 m in diameter, with the pulse lasting for 4.0 ns with an average power of 2.0x10 12 W. We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse. a) How much energy is given to the cell during this pulse? b) What is the intensity (in W/m 2 ) delivered to the cell? c) What are the maximum values of the electric and magnetic fields in the pulse? Recall that power is energy/time. So 2.0x10 12 W is 2.0x10 12 Joules/sec. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB This is the total energy, which is spread out over 100 cells, so the energy for each individual cell is 80 Joules. Slide 15 Example: High-Energy Cancer Treatment Scientists are working on a technique to kill cancer cells by zapping them with ultrahigh- energy pulses of light that last for an extremely short amount of time. These short pulses scramble the interior of a cell without causing it to explode, as long pulses do. We can model a typical such cell as a disk 5.0 m in diameter, with the pulse lasting for 4.0 ns with an average power of 2.0x10 12 W. We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse. a) How much energy is given to the cell during this pulse? b) What is the intensity (in W/m 2 ) delivered to the cell? c) What are the maximum values of the electric and magnetic fields in the pulse? To get intensity, we need to divide power/area. The area for a cell is just the area of a circle: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 16 Example: High-Energy Cancer Treatment Scientists are working on a technique to kill cancer cells by zapping them with ultrahigh- energy pulses of light that last for an extremely short amount of time. These short pulses scramble the interior of a cell without causing it to explode, as long pulses do. We can model a typical such cell as a disk 5.0 m in diameter, with the pulse lasting for 4.0 ns with an average power of 2.0x10 12 W. We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse. a) How much energy is given to the cell during this pulse? b) What is the intensity (in W/m 2 ) delivered to the cell? c) What are the maximum values of the electric and magnetic fields in the pulse? To get intensity, we need to divide power/area. The area for a cell is just the area of a circle: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Now divide to get intensity: This is the total area of all 100 cells. Slide 17 Example: High-Energy Cancer Treatment Scientists are working on a technique to kill cancer cells by zapping them with ultrahigh- energy pulses of light that last for an extremely short amount of time. These short pulses scramble the interior of a cell without causing it to explode, as long pulses do. We can model a typical such cell as a disk 5.0 m in diameter, with the pulse lasting for 4.0 ns with an average power of 2.0x10 12 W. We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse. a) How much energy is given to the cell during this pulse? b) What is the intensity (in W/m 2 ) delivered to the cell? c) What are the maximum values of the electric and magnetic fields in the pulse? To get the field strengths, recall our formulas: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Slide 18 Example: High-Energy Cancer Treatment Scientists are working on a technique to kill cancer cells by zapping them with ultrahigh- energy pulses of light that last for an extremely short amount of time. These short pulses scramble the interior of a cell without causing it to explode, as long pulses do. We can model a typical such cell as a disk 5.0 m in diameter, with the pulse lasting for 4.0 ns with an average power of 2.0x10 12 W. We shall assume that the energy is spread uniformly ove

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