Q37PE Show that for a continuous sinus... [FREE SOLUTION]

Chapter 24: Q37PE (page 889)

Show that for a continuous sinusoidal electromagnetic wave, the peak intensity is twice the average intensity $(I_{0} = 2 I_{ave})$ , using either the fact that $E_{0} = \sqrt{2 E_{rms}}, or B_{0} = \sqrt{2 B_{rms}}$ , where rms means average (actually root mean square, a type of average).

Short Answer

Expert verified

The solution is $I_{0} = 2 I_{avg}$ .

Step by step solution

Define electromagnetic waves

Electromagnetic waves, or EM waves, are waves that are formed when an electric field and a magnetic field vibrate together.

Explanation

It is known that a wave's intensity is related to its amplitude squared and is given by

$I_{0} = {kE}_{0}^{2}$

Where $I_{0}$ is peak intensity, k is proportionality constant, $E_{0}$ is peak electric field strength.

And the average intensity is calculated as

$I_{avg} = {kE}_{rms}^{2}$

Where $I_{avg}$ is average intensity, k is proportionality constant, $E_{rms}$ is average electric field strength.

Therefore,

$\frac{I_{0}}{I_{avg}} = \frac{{kE}_{0}^{2}}{{kE}_{rms}^{2}}$

Substitute the value of $E_{0} = \sqrt{2 E_{rms}}$ in the above equation,

$\frac{I_{0}}{I_{avg}} = \frac{{kE}_{0}^{2}}{{kE}_{rms}^{2}} \frac{I_{0}}{I_{avg}} = \frac{{(\sqrt{2} E_{rms})}^{2}}{{E_{rms}}^{2}} \frac{I_{0}}{I_{avg}} = 2 I_{0} = 2 I_{avg} Therefore, I_{0} = 2 I_{avg} .$

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91影视

Show that for a continuous sinusoidal electromagnetic wave, the peak intensity is twice the average intensity $(I_{0} = 2 I_{ave})$ , using either the fact that $E_{0} = \sqrt{2 E_{rms}}, or B_{0} = \sqrt{2 B_{rms}}$ , where rms means average (actually root mean square, a type of average).

Short Answer

Step by step solution

Define electromagnetic waves

Explanation

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91影视

Show that for a continuous sinusoidal electromagnetic wave, the peak intensity is twice the average intensity (I0=2Iave), using either the fact that E0=2Erms,orB0=2Brms, where rms means average (actually root mean square, a type of average).

Short Answer

Step by step solution

Define electromagnetic waves

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Scientific Method Physics

Radiation

Space Physics

Physical Quantities And Units

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

Show that for a continuous sinusoidal electromagnetic wave, the peak intensity is twice the average intensity $(I_{0} = 2 I_{ave})$ , using either the fact that $E_{0} = \sqrt{2 E_{rms}}, or B_{0} = \sqrt{2 B_{rms}}$ , where rms means average (actually root mean square, a type of average).