* EST A microwave oven produces
(a) Determine the wavelength of the microwaves, (b) estimate the amplitude of the
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- You may wish to review Sections 16.4 and 16.8 on the transport of energy by string waves and sound. Figure P33.46 is a graphical representation of an electromagnetic wave moving in the x direction. We wish to find an expression for the intensity of this wave by means of a different process from that by which Equation 33.27 was generated. (a) Sketch a graph of the electric field in this wave at the instant t = 0, letting your flat paper represent the xy plane. (b) Compute the energy density uE in the electric field as a function of x at the instant t = 0. (c) Compute the energy density in the magnetic field uB as a function of x at that instant. (d) Find the total energy density u as a function of x, expressed in terms of only the electric field amplitude. (e) The energy in a shoebox of length and frontal area A is E=0uAdx. (The symbol E for energy in a wavelength imitates the notation of Section 16.4.) Perform the integration to compute the amount of this energy in terms of A, , Emax, and universal constants. (f) We may think of the energy transport by the whole wave as a series of these shoeboxes going past as if carried on a conveyor belt. Each shoebox passes by a point in a time interval defined as the period T = 1/f of the wave. Find the power the wave carries through area A. (g) The intensity of the wave is the power per unit area through which the wave passes. Compute this intensity in terms of Emax and universal constants. (h) Explain how your result compares with that given in Equation 33.27. Figure P33.46arrow_forwardUnreasonable Results A researcher measures the wavelength of a 1.20-GHz electromagnetic wave to be 0.500 m. (a) Calculate the speed at which this wave propagates. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?arrow_forwardSuppose the maximum safe intensity of microwaves for human exposure is taken to be 1.00 W/m2. (a) If a radar unit leaks 10.0 W of microwaves (other than those sent by its antenna) uniformly in all directions, how far away must you be to be exposed to an intensity considered to be safe? Assume that the power spreads uniformly over the area of a sphere with no complications from absorption or reflection. (b) What is the maximum electric field strength at the safe intensity? (Note that early radar units leaked more than modern ones do. This caused identi?able health problems, such as cataracts, for people who worked near them.)arrow_forward
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- A dish antenna with a diameter of 20.0 m receives (at normal incidence) a radio signal from a distant source, as shown in Figure P21.73. The radio signal is a continuous sinusoidal wave with amplitude Emax = 0.20 V/m. Assume the antenna absorbs all the radiation that falls on the dish. (a) What is the amplitude of the magnetic field in this Figure P21.73 wave? (b) What is the intensity of the radiation received by the antenna? (c) What is the power received by the antenna?arrow_forwardA particle of cosmic dust has a density =2.0g/cm3 , (a) Assuming the dust particles are spherical and light absorbing, and are at the same distance as Earth from the Sun, determine the particle size for which radiation pressure from sunlight is equal to the Sun's force of gravity on the dust particle, (b) Explain how the forces compare if the particle radius is smaller, (c) Explain what this implies about the sizes of dust particle likely to be present in the inner solar system compared with outside the Oort cloud.arrow_forwardA plane electromagnetic wave of frequency 20 GHz moves in the positive y-axis direction such that its electric field is pointed along the z-axis. The amplitude of the electric field is 10 V/m. The start of time is chosen so that at t = 0, the electric field has a value 10 V/m at the origin. (a) Write the wave function that will describe the electric field wave, (b) Find the wave function that will describe the associated magnetic field wave.arrow_forward
- A large, flat sheet carries a uniformly distributed electric current with current per unit width Js. This current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B=120Js. If the current is in the y direction and oscillates in time according to Jmax(cost)j=Jmax[cos(t)]j the sheet radiates an electromagnetic wave. Figure P33.28 shows such a wave emitted from one point on the sheet chosen to be the origin. Such electromagnetic waves arc emitted from all points on the sheet. The magnetic field of the wave to the right of the sheet is described by the wave function B=120Jmax[cos(kxt)]k (a) Find the wave function for the electric field of the wave to the right of the sheet. (b) Find the Poynting vector as a function of x and t. (c) Find the intensity of the wave. (d) What If? If the sheet is to emit radiation in each direction (normal to the plane of the sheet) with intensity 570 W/m2, what maximum value of sinusoidal current density is required? Figure P33.28arrow_forwardConsider a small, spherical particle of radius r located in space a distance R from the Sun, of mass MS. Assume the particle has a perfectly absorbing surface and a mass density . The value of the solar intensity at the particles location is S. Calculate the value of r for which the particle is in equilibrium between the gravitational force and the force exerted by solar radiation. Your answer should be in terms of S, R, , and other constants.arrow_forwardRadio waves normally have their E and B fields in specific directions, whereas visible light usually has its E and B fields in random and rapidly changing directions that are perpendicular to each other and to the propagation direction. Can you explain why?arrow_forward
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