Consider two identical antennas separated by 9.00 m that radiate in phase at 120 MHz. A receiver placed 150 m from both antennas measures an intensity I0. The receiver is moved so that it is 1.8 m closer to one antenna than to the other. a) What is the phase difference ϕ between the two radio waves produced by this path difference? b) In terms of I0, what is the intensity measured by the receiver at its new position?

A microwave source produces pulses of 20.0-GHz radiation, with each pulse lasting 1.00 ns. A parabolic reflector with a face area of radius 6.00 cm is used to focus the micro-waves into a parallel beam of radiation as shown in Figure P24.72. The average power during each pulse is 25.0 kW. (a) What is the wavelength of these microwaves? (b) What is the total energy contained in each pulse? (c) Compute the average energy density inside each pulse. (d) Determine the amplitude of the electric and magnetic fields in these microwaves. (e) Assuming that this pulsed beam strikes an absorbing surface, compute the force exerted on the surface during the 1.00-ns duration of each pulse.

A microwave source produces pulses of 20.0GHz radiation, with each pulse lasting 1.00 ns. A parabolic reflector with a face area of radius 6.00 cm is used to focus the microwaves into a parallel beam of radiation as shown in Figure P34.60. The average power during each pulse is 25.0 kW. (a) What is the wavelength of these microwaves? (b) What is the total energy contained in each pulse? (c) Compute the average energy density inside each pulse. (d) Determine the amplitude of the electric and magnetic fields in these microwaves. (e) Assuming that this pulsed beam strikes an absorbing surface, compute the force exerted on the surface during the 1.00-ns duration of each pulse. Figure P34.60

The electric field of an electromagnetic wave traveling in vacuum is described by the following wave function: E =(5.00V/m)cos[kx(6.00109s1)t+0.40] j where k is the wavenumber in rad/m, x is in m, t s in Find the following quantities: (a) amplitude (b) frequency (c) wavelength (d) the direction of the travel of the wave (e) the associated magnetic field wave

(a) The ideal size (most efficient) for a broadcast antenna with one end on the ground is onefourth the wavelength (/4) of the electromagnetic radiation being sent out. If a new radio station has such an antenna that is 50.0 m high, what frequency does it broadcast most efficiently? Is this in the AM or FM band? (b) Discuss the analogy of the fundamental resonant mode of an air column closed at one end to the resonance of currents on an antenna that is one-fourth their wavelength.

The following represents an electromagnetic wave traveling in the direction of the positive y-axis: Ex=0;E0cos(kxt);Ez=0Bx=0;By=0;Bz=B0cos(kxt) The wave is passing through a wide tube of circular cross- section of radius R whose axis is along they-axis. Find the expression for the displacement current through the tube.

A dish antenna having a diameter of 20.0 m receives (at normal incidence) a radio signal from a distant source as shown in Figure P34.65. The radio signal is a continuous sinusoidal wave with amplitude Emax = 0.200 V/m. Figure P34.65 Assume the antenna absorbs all the radiation that falls on the dish. (a) What is the amplitude of the magnetic field in this wave? (b) What is the intensity of the radiation received by this antenna? (c) What is the power received by the antenna? (d) What force is exerted by the radio waves on the antenna?

Figure P36.35 shows a radio-wave transmitter and a receiver separated by a distance d = 50.0 m and both a distance h = 35.0 m above the ground. The receiver can receive signals both directly from the transmitter and indirectly from signals that reflect from the ground. Assume the ground is level between the transmitter and receiver and a 180 phase shift occurs upon reflection. Determine the longest wavelengths that interfere (a) constructively and (b) destructively. Figure P36.35 Problems 35 and 36.

In Figure P37.52, suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also, let the center disk be rotated on the common axis with an angular speed . Show that if unpolarized light is incident on the left disk with an intensity Imax, the intensity of the beam emerging from the right disk is I=116Imax(1cos4t) This result means that the intensity of the emerging beam is modulated at a rate four times the rate of rotation of the center disk. Suggestion: Use the trigonometric identities cos2=12(1+cos2) and sin2=12(1cos2). Figure P37.52

A linearly polarized microwave of wavelength 1.50 cm is directed along the positive x axis. The electric field vector has a maximum value of 175 V/m and vibrates in the xy plane. Assuming the magnetic field component of the wave can be written in the form B = Bmax sin (kx t), give values for (a) Bmax, (b) k, and (c) . (d) Determine in which plane the magnetic field vector vibrates. (e) Calculate the average value of the Poynting vector for this wave. (f) If this wave were directed at normal incidence onto a perfectly reflecting sheet, what radiation pressure would it exert? (g) What acceleration would be imparted to a 500-g sheet (perfectly reflecting and at normal incidence) with dimensions of 1.00 m 0.750 m?