+y +z Consider the three-dimensional coordinate system above. If at one point in time an electromagnetic wave is moving in the -x direction and has its E-field in the -z direction, in which direction is the B-field at the same point in time? O -x direction O -z direction O +x direction

Integrated Concepts Electromagnetic radiation from a 5.00-mw laser is concentrated on a 1.00m2 area. (a) What is the intensity in W/m2? (b) Suppose a 2.00nC static charge is in the beam. What is me maximum electric force it experience? (c) If the static charge moves at 400 m/s, what maximum magnetic force can it feel?

If you wish to detect details of the size of atoms (about 0.2 nm) with electromagnetic radiation, it must have a wavelength of about this size. (a) What is its frequency? (b) What type of electromagnetic radiation might this be?

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 P33.46

Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time—called pulsed lasers. They are used to initiate nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of 1.001011 V/m for a time of 1.00 ns. (a) What is the maximum magnetic field strength in the wave? (b) What is the intensity of the beam? (c) What energy does it deliver on an 1.00-mm2 area?

In which situation shown in Figure 24.24 will the electromagnetic wave be more successful in inducing a current in the wire? Explain. Figure 24.24 Electromagnetic waves approaching long straight wiles.

Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time-called pulsed lasers. They are used to ignite nuclear fusion, for example. Such a lager may produce an electromagnetic wave with a maximum electric field strength of 1.001011V/m for a time of 1.00 ns. (a) What is the maximum magnetic field strength in the wave? (b) What is the intensity of the beam? (c) What energy does it deliver on a 1.00-mm2 area?

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 P33.28

Review. A microwave oven is powered by a magnetron, an electronic device that generates electromagnetic waves of frequence 2.45 GHz. The microwaves enter the oven and arc reflected by the walls. The standing-wave pattern produced in the oven can cook food unevenly, with hot spots in the food at antinodes and cool spots at nodes, so a turntable is often used to rotate the food and distribute the energy. If a microwave oven intended for use with a turntable is instead used with a cooking dish in a fixed position, the antinodes can appear as burn marks on foods such as carrot strips or cheese. The separation distance between the burns is measured to be 6 cm 5%. From these data, calculate the speed of the microwaves.

A community plans to build a facility to convert solar radiation to electrical power. The community requires 1.00 MW of power, and the system to be installed has an efficiency of 30.0% (that is, 30.0% of the solar energy incident on the surface is converted to useful energy that can power the community). Assuming sunlight has a constant intensity of 1 000 W/m2, what must be the effective area of a perfectly absorbing surface used in such an installation?