ism_chapter_30 - Chapter 30 Maxwell's Equations and...

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815 Chapter 30 Maxwell’s Equations and Electromagnetic Waves Conceptual Problems *1 ( a ) False. Maxwell’s equations apply to both time-independent and time-dependent fields. ( b ) True ( c ) True ( d ) True ( e ) False. The magnitudes of the electric and magnetic field vectors are related according to E = cB . ( f ) True 2 •• Determine the Concept Two changes would be required. Gauss’s law for magnetism would become m 0 S n q dA B µ = and Faraday’s law would become 0 m S n C I dA B dt d d = l r r E , where I m is the current associated with the motion of the magnetic poles. 3 Determine the Concept X rays have greater frequencies whereas light waves have longer wavelengths (see Table 30-1). *4 Determine the Concept The frequencies of ultraviolet radiation are greater than those of infrared radiation (see Table 30-1). 5 Determine the Concept Consulting Table 30-1 we see that FM radio and televisions waves have wavelengths of the order of a few meters. 6 Determine the Concept The dipole antenna detects the electric field, the loop antenna detects the magnetic field of the wave.
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Chapter 30 816 7 Determine the Concept The dipole antenna should be in the horizontal plane and normal to the line from the transmitter to the receiver. *8 Determine the Concept A red plastic filter absorbs all the light incident on it except for the red light and a green plastic filter absorbs all the light incident on it except for the green light. If the red beam is incident on a red filter it will pass through, whereas, if it is incident on the green filter it will be absorbed. Because the green filter absorbs more energy than does the red filter, the laser beam will exert a greater force on the green filter. Estimation and Approximation 9 •• Picture the Problem We’ll assume that the plastic bead has the same density as water. Applying a condition for translational equilibrium to the bead will allow us to relate the gravitational force acting on it to the force exerted by the laser beam. Because the force exerted by the laser beam is related to the radiation pressure and the radiation pressure to the intensity of the beam, we’ll be able to find the beam’s intensity. Knowing the beam’s intensity, we find the total power needed to lift the bead. Apply 0 = y F to the bead: 0 beam laser by = mg F Relate the force exerted by the laser beam to the radiation pressure exerted by the beam: r 2 r beam laser by 4 1 P d A P F π = = Substitute to obtain: 0 4 1 r 2 = mg P d The radiation pressure P r is the quotient of the intensity I and the speed of light c : c I P = r Substitute for P r to obtain: 0 4 1 2 = mg c I d (1) Express the mass of the bead: 3 6 1 d V m πρ ρ = = Substitute for m in equation (1) to obtain: 0 6 1 4 1 3 2 = g d c I d
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Maxwell’s Equations and Electromagnetic Waves 817 Solve for I : dg c I ρ 3 2 = Substitute numerical values and evaluate I : () ( ) ( ) 2 7 2 3 3 8 W/m 10 94 . 2 m/s 81 . 9 15 kg/m 10 m/s 10 3 3 2 × = × = m I µ The power needed is the product of the beam intensity and the cross-
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ism_chapter_30 - Chapter 30 Maxwell's Equations and...

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