![]() ![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Paul Peter Urone, Roger Hinrichs Use the information below to generate a citation. Then you must include on every digital page view the following attribution: ![]() ![]() If you are redistributing all or part of this book in a digital format, The constant was postulated by Max Planck in 1900 as a proportionality constant needed to explain experimental black-body radiation. Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. In fact, for a continuous sinusoidal electromagnetic wave, the average intensity I ave I ave is given by Thus the energy carried and the intensity I I of an electromagnetic wave is proportional to E 2 E 2 and B 2 B 2. In electromagnetic waves, the amplitude is the maximum field strength of the electric and magnetic fields. This is true for waves on guitar strings, for water waves, and for sound waves, where amplitude is proportional to pressure. Clearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries.Ī wave’s energy is proportional to its amplitude squared ( E 2 E 2 or B 2 B 2 ). If absorbed, the field strengths are diminished and anything left travels on. Once created, the fields carry energy away from a source. With electromagnetic waves, larger E E-fields and B B-fields exert larger forces and can do more work.īut there is energy in an electromagnetic wave, whether it is absorbed or not. Integrated Concepts. On its highest power setting, a microwave oven increases the temperature of 0.400 kg of spaghetti by 45.0✬ in 120 s.Figure 24.22 Energy carried by a wave is proportional to its amplitude squared.(d) How long will it take to increase the temperature of the 4.00-kg shoulder by 2.00º C, assuming no other heat transfer and given that its specific heat is 3.47 × 10 3 J/kg⋅✬? (a) If the lamp’s 200-W output is focused on a person’s shoulder, over a circular area 25.0 cm in diameter, what is the intensity in W/m 2? (b) What is the peak electric field strength? (c) Find the peak magnetic field strength. Integrated Concepts.Assume the mostly infrared radiation from a heat lamp acts like a continuous wave with wavelength 1.50μm.If 1.50 × 10 9-Hz microwaves are used and a beat frequency of 150 Hz is produced, what is the speed of the vehicle? (Assume the same Doppler-shift formulas are valid with the speed of sound replaced by the speed of light.) Beats are produced by mixing the double Doppler-shifted echo with the original frequency. Integrated Concepts. Police radar determines the speed of motor vehicles using the same Doppler-shift technique employed for ultrasound in medical diagnostics.Integrated Concepts. What capacitance is needed in series with an 800- μH inductor to form a circuit that radiates a wavelength of 196 m?.(a) What is the resonant frequency? (b) What inductance is in series with the capacitor? Integrated Concepts. An LC circuit with a 5.00-pF capacitor oscillates in such a manner as to radiate at a wavelength of 3.30 m.(b) Show that the magnitudes of the electric and magnetic fields are inversely proportional to r. (a) Show that the intensity is inversely proportional to r 2, the distance from the source squared. Suppose a source of electromagnetic waves radiates uniformly in all directions in empty space where there are no absorption or interference effects.(3.46) and (5.110): Moreover, let us assume for a while, that these constitutive equations hold for all frequencies of interest. \displaystyle\\, where rms means average (actually root mean square, a type of average). Let us start from considering a spatial region that does not contain field sources ( 0, j 0), and is filled with a linear, uniform, isotropic medium, which obeys Eqs. In fact, for a continuous sinusoidal electromagnetic wave, the average intensity I ave is given by Thus the energy carried and the intensity I of an electromagnetic wave is proportional to E 2 and B 2. Clearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries.Ī wave’s energy is proportional to its amplitude squared ( E 2 or B 2). With electromagnetic waves, larger E-fields and B-fields exert larger forces and can do more work.īut there is energy in an electromagnetic wave, whether it is absorbed or not. Energy carried by a wave is proportional to its amplitude squared. ![]()
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