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Chapter 33: Q1Q (page 1000)

If the magnetic field of a light wave oscillates parallel to a y axis and is given byBy=Bmsin(kz-蝇t), (a) in what direction does the wave travel and (b) parallel to which axis does the associated electric field oscillate?

Short Answer

Expert verified

(a) The direction of wave travel is along the z-axis.

(b) The direction of oscillation of the electric field is along the x-axis.

Step by step solution

01

The given data

The equation of the magnetic field oscillating parallel to the y axis is given as:

By=Bmsinkz-蝇t

02

Understanding the concept of electromagnetic wave

An electromagnetic wave consists of an electric field and a magnetic field, and the direction of the propagating electromagnetic wave is perpendicular to the plane in which the electric field and magnetic field lie. Thus, by analyzing the given equation, we can find the direction of the electromagnetic wave and the direction of the electric field component.

03

a) Calculation of the direction of wave

From the given equation, the term "kz" denotes that the wave travels along the z 鈥揹irection.

Hence, the direction of the wave is towards the z-axis.

04

b) Calculation of the direction of the electric field component

As the magnetic field is oscillating parallel to the y axis and the wave is traveling along the z direction. Thus, we can say that the electric field must oscillate parallel to the x-axis, perpendicular to both the directions of the propagation of the wave and the magnetic field.

Hence, the direction of the component of the electric field is towards the x-axis.

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Most popular questions from this chapter

In Fig. 33-73, a long, straight copper wire (diameter2.50鈥尘尘 and resistance1.00鈥坝﹑别谤300鈥尘 ) carries a uniform current of 25鈥碱in the positive x direction. For point P on the wire鈥檚 surface, calculate the magnitudes of (a) the electricfield,E鈫�(b) the magnetic field , B鈫�and (c) the Poynting vector S鈫�, and (d) determine the direction of S鈫�.

Radiation from the Sun reaching Earth (just outside the atmosphere) has an intensity of 1.4kW/m2. (a) Assuming that Earth (and its atmosphere) behaves like a flat disk perpendicular to the Sun鈥檚 rays and that all the incident energy is absorbed, calculate the force on Earth due to radiation pressure. (b) For comparison, calculate the force due to the Sun鈥檚 gravitational attraction.

In Fig. 33-47a, a light ray in an underlying material is incident at an angleon a boundary with water, and some of the light refracts into the water. There are two choices of the underlying material. For each, the angle of refractionversus the incident angleis given in Fig. 33-47b.The horizontal axis scale is set by胃1s=90掳.Without calculation, determine whether the index of refraction of

(a) material1 and

(b) material2 is greater or less than the index of water(n=1.33).What is the index of refraction of

(c) material 1 And

(d) material 2?

In Fig. 33-41, a beam of light, with intensity43鈥塛/尘2and polarization parallel to a y-axis, is sent into a system of two polarizing sheets with polarizing directions at angles of 胃1=70掳and 胃2=90掳to the y axis. What is the intensity of the light transmitted by the two-sheet system?

The primary rainbow described in Problem 77 is the type commonly seen in regions where rainbows appear. It is produced by light reflecting once inside the drops. Rarer is the secondary rainbow described in Module 33-5, produced by light reflecting twice inside the drops (Fig. 33-68a). (a) Show that the angular deviation of light entering and then leaving a spherical water drop is胃dev=(180掳)k+2胃i-2(k+1)胃r

where, k is the number of internal reflections. Using the procedure of Problem 77, find the angle of minimum deviation for (b) red light and (c) blue light in a secondary rainbow. (d) What is the angular width of that rainbow (Fig. 33-21d)?

The tertiary rainbow depends on three internal reflections (Fig. 33-68b). It probably occurs but, as noted in Module 33-5, cannot be seen with the eye because it is very faint and lies in the bright sky surrounding the Sun. What is the angle of minimum deviation for (e) the red light and (f) the blue light in this rainbow? (g) What is the rainbow鈥檚 angular width?
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