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  1. Fig.2 x-axis linear polarization 12 Thus, the similar polarization of electric field on only a specific straight direction is defined as linear polarization. On the other hand, Assume E y equals to zero, which gives the electric field as:

  2. We can always define the zˆ direction as where k points. When we put a hat on a vector, it means the unit vector pointing in that direction, that is zˆ = (0, 0, 1). Thus the electric field has the form E0eiω. z E = −t. c. (5) which moves in the z direction at the speed of light.

  3. The distance between successive wavefronts at 2π phase intervals is λo in the direction of propagation, and the distances separating these same wavefronts as measured along the x and z axes are equal or greater, as illustrated in Figure 9.2.1. For example: λ z = λo cos θ = 2π kz ≥ λo.

  4. By selecting the proper initial displacement and initial velocity, we can set the ball in oscillation along either the $x$-axis or the $y$-axis, or along any straight line in the $xy$-plane. These motions of the ball are analogous to the oscillations of the electric field vector illustrated in Fig. 33–1 .

  5. In order to satisfy all four equations, the waves must have the E and B fields transverse to the propagation direction. Thus, if the wave is traveling along the positive z-axis, the electric field can be parallel to the +x-axis and B-field parallel to +y. Half a cycle later, E and B are parallel to –x and –y.

  6. Explain how Maxwell’s equations predict that the speed of propagation of electromagnetic waves in free space is exactly the speed of light. Calculate the relative magnitude of the electric and magnetic fields in an electromagnetic plane wave. Describe how electromagnetic waves are produced and detected.

  7. That is why we call these waves transverse electromagnetic (TEM) waves. We consider the electric field of a monochromatic electromagnetic wave with frequency ω and electric field amplitude E0, which propagates in vacuum along the z-axis, and is polarized along the x-axis, (Fig. 2.1), i.e. | k k| = ez, and e( k)= e x. ThenweobtainfromEqs.(2. ...

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