Calculating the components of an electromagnetic wave

In summary, the problem presents an electromagnetic planewave propagating in vacuum along the positive x axis with an electric field vector parallel to the y axis. The component E_y is dependent on the variable x at t = 0 and is equal to E_0 if |x + a| < b, and 0 if |x + a| > b. The problem also includes an ideal plane mirror placed at x = 0 and asks for the components of the electric and magnetic field at three different time instants: t_1 = a/2c, t_2 = a/c, and t_3 = 2a/c. The solution involves finding the E_y behavior at these times and multiplying it by 1
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Homework Statement



An electromagnetic planewave (non-monochromatic) propagates in vacuum along the positive x axis. The electric field vector is parallel to the y axis. We know the dependence of the component [itex]E_y[/itex] on the variable [itex]x[/itex] at the moment [itex]t = 0[/itex]:

[itex]E_y(x) = E_0\ \text{if}\ |x + a| < b[/itex]
[itex]E_y(x) = 0\ \text{if}\ |x + a| > b[/itex]

[itex]a/2 > b > 0[/itex]

An ideal plane mirror is placed at [itex]x = 0[/itex]. Find the components of the electric and magnetic field as functions of the variable at the following time instants: [itex]t_1 = a/2c,\ t_2 = a/c,\ t_3 = 2a/c[/itex].

Homework Equations



One dimensional electromagnetic planewave propagating in the positive x direction:

[itex]E = E(x - ct)[/itex]
[itex]B= (1/c)E[/itex]


The Attempt at a Solution



As the wave propagates in the x direction, and the electric field is in the y direction, the magnetic field only has a nonzero component in the z direction. So all I have to do is find the [itex]E_y[/itex] behavior at the given times and multiply it by [itex]1/c[/itex].

Let [itex]a = ct[/itex]. Then, for any time greater than zero, the electric field is null, because [itex]a[/itex] is always greater than [itex]b[/itex], and [itex]x[/itex] is always positive, so [itex]|x + a|[/itex] has to be greater than [itex]b[/itex]. So it is a wave that exists only when [itex]t = 0[/itex] for certain values of [itex]x[/itex], and vanishes for any [itex]t > 0[/itex] or any [itex]x > b[/itex]. But what is the purpose of a exercise like this if the wave does not exist at the given times?

Am I wrong? How can I use the information about the mirror?
 
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  • #2
Anyone? I asked my professor about this question, and he said to me that [itex]|x + a|[/itex] is the distance between the mirror and the wave, centered at [itex]a[/itex], and [itex]2b[/itex] is the length of the wave. But now I am even more confused.
 

FAQ: Calculating the components of an electromagnetic wave

1. What are the components of an electromagnetic wave?

The components of an electromagnetic wave are the electric field and the magnetic field. These fields are perpendicular to each other and also to the direction of wave propagation.

2. How do you calculate the wavelength of an electromagnetic wave?

The wavelength of an electromagnetic wave can be calculated using the formula λ = c/f, where λ is the wavelength, c is the speed of light (3 x 108 m/s), and f is the frequency of the wave in hertz (Hz).

3. What is the relationship between frequency and energy of an electromagnetic wave?

The energy of an electromagnetic wave is directly proportional to its frequency. This means that higher frequency waves have more energy than lower frequency waves.

4. How do you determine the amplitude of an electromagnetic wave?

The amplitude of an electromagnetic wave is determined by the strength of the electric and magnetic fields. The larger the amplitude, the stronger the fields and the more energy the wave carries.

5. Can you calculate the speed of an electromagnetic wave?

Yes, the speed of an electromagnetic wave can be calculated using the formula c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. This formula shows that the speed of an electromagnetic wave is constant and equal to the speed of light.

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