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LC Circuit There is a characteristic frequency at which the circuit will oscillate, called the resonance frequency Section 22.5 LRC Circuits and Resonance From Kirchhoff’s Loop Rule, VAC = VL + VC + VR But the voltages are not all in phase All the current phasors are in the same direction Max current depends of frequency of source Section 22.6 LRC Circuits and Resonance Section 22.6 LRC Circuits and Resonance At most frequencies, the source voltage is out of sync with the natural flow of energy in the circuit Natural flow governed by LC portion Current in circuit is reduced At the resonance frequency, the source voltage and the natural flow of energy oscillate together XL=XC Synchronization occurs at the resonance frequency of the LC circuit Section 22.7 Electromagnetic Waves Electromagnetism Electricity and magnetism are coupled Changing electric field create magnetic fields Changing magnetic fields create electric fields Energy exists in fields Fills “empty” space Energy density proportional to square of field Introduction Electromagnetic Waves Self-sustaining oscillations involving E and B are possible Both fields must be changing with time The fields are perpendicular to each other The propagation direction of the wave is perpendicular to both the electric field and the magnetic field Section 23.1 Electromagnetic Waves Electromagnetic waves (or radiation) travel at a characteristic speed The speed of an EM wave is denoted by c c0 = 3.00 x 108 m/s The value of the speed of an electromagnetic wave is the same as the speed of light Light is a visible electromagnetic wave Section 23.2 Electromagnetic Waves EM waves can travel through empty space Always travel with speed c0 through empty The frequency and wavelength are determined by the way the wave is produced When an EM wave travels through a material substance, its speed depends on the properties of the substance The speed of the wave is always less than c0 The speed of the wave depends on the wave’s frequency Section 23.2 Electromagnetic Waves The wave carries energy utotal = uelec + umag uelec 1 1 2 o E 2 and umag B 2 2 o As the wave propagates, the energies per unit volume oscillate The electric and magnetic energies are equal Peak electric and magnetic fields are proportional Section 23.3 Intensity The strength of an EM wave is usually measured in terms of its intensity Intensity is the amount of energy transported per unit time across a surface of unit area Intensity also equals the energy density multiplied by the speed of the wave I = utotal × c = ½ εo c Eo2 Since E = c B, the intensity is also proportional to the square of the magnetic field amplitude Section 23.3 Radiation Pressure EM waves carry momentum The momentum of the wave is When an electromagnetic wave is absorbed by an object, it exerts a force on the object The total force on the object is proportional to its exposed area Radiation pressure is the force of the electromagnetic force divided by the area This can also be expressed in terms of the intensity Pradiation F I A c Section 23.3 Polarization E and B fields can oscillate in many directions with the same direction of propagation If all E fields (and all B fields) oscillate in the same direction, the EM waves are polarized E and B fields are still perpendicular to each other Most light is unpolarized Polarized light can be created using a polarizer Defined by polarization axis Section 23.6 Polarization If the electric field is parallel to the polarizer’s axis: Eout = Ein If the electric field is perpendicular to the polarizer’s axis, Eout = 0 If the electric field makes some angle θ relative to the polarizer’s axis, Eout = Ein cos θ Polarization This relationship can be expressed in terms of intensity in the Law of Malus: Iout = Iin cos2 θ Unpolarized light can be thought of as a collection of many separate light waves, each linearly polarized in different and random directions The average outgoing intensity is the average of all the incident waves: Iout = (Iin cos2 θ)ave = ½ Iin Electromagnetic Spectrum Electromagnetic waves are classified according to their frequency and wavelength The wave equation is true for EM waves: The range of all possible electromagnetic waves is called the electromagnetic spectrum Section 23.4 Radio Waves Frequencies from a few hertz up to about 109 hertz Corresponding wavelengths are from about 108 meters to a few centimeters Usually produced by an AC circuit attached to an antenna A simple wire can function as an antenna Antennas containing multiple conducting elements or shaped as “dishes” are usually more efficient and more common Radio waves can be detected by an antenna similar to the one used for generation Microwaves Microwaves have frequencies between about 109 Hz and 1012 Hz Corresponding wavelengths are from a few cm to a few tenths of a mm Microwave ovens generate radiation with a frequency near 2.5 x 109 Hz The microwave energy is transferred to water molecules in the food, heating the food Section 23.4 Infrared Infrared radiation has frequencies from about 1012 Hz to 4 x 1014 Hz Wavelengths from a few tenths of a mm to a few microns We sense this radiation as heat Blackbody radiation from objects near room temperature falls into this range Also useful for monitoring Section 23.4 Visible Light Frequencies from about 4 x1014 Hz to 8 x1014 Hz Wavelengths from about 750 nm to 400 nm The color of the light varies with the frequency Low frequency; high wavelength – red High frequency; low wavelength – blue The speed of light inside a medium depends on the frequency of the radiation The effect is called dispersion White light is separated into different colors Section 23.4 Ultraviolet Ultraviolet (UV) light has frequencies from about 8 x 1014 Hz to 1017 Hz Corresponding wavelengths are about 3 nm to 400 nm UV radiation stimulates the production of vitamin D in the body Excessive exposures to UV light can cause sunburn, skin cancer and cataracts Section 23.4 X-Rays Frequencies from about 1017 Hz to about 1020 Hz Discovered by Wilhelm Röntgen in 1895 X-rays are weakly absorbed by skin and other soft tissue and strongly absorbed by dense material such as bone, teeth, and metal In the 1970’s CT (CAT) scans were developed Section 23.4 Gamma Rays Gamma rays are the highest frequency electromagnetic waves, with frequencies above 1020 Hz Wavelengths are less than 10-12 m Gamma rays are produced by processes inside atomic nuclei They are produced in nuclear power plants and in the Sun Gamma rays also reach us from outside the solar system Section 23.4
