Chapter 4: Q28E (page 1074)

A laser beam has diameter 1.20 mm. What is the amplitude of the electric field of the electromagnetic radiation in this beam if the beam exerts a force of $3.8 \times 10^{- 9} N$ on a totally reflecting surface?

Short Answer

Expert verified

The amplitude of the electric field of the electromagnetic radiation is $1.95 \times 10^{4} V / m$ .

Step by step solution

Radiation pressure exerted by electromagnetic wave

Radiation pressure is mechanical pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field.

The Radiation pressure exerted by electromagnetic wave is given by

$p_{r a d} = \frac{2 I}{c}$

Where, $p_{r a d}$ is the radiation pressure, I is the intensity and C is the speed of light.

Intensity of electromagnetic wave

Intensity of electromagnetic wave in terms of electric field

$I = \frac{1}{2} ε_{0} c {E^{2}}_{m a x^{}}$

Where, $ε_{0}$ is the permittivity of vacuum ,role="math" localid="1664425325176" $E_{m a x}$ is the maximum amplitude of electric field and C is the speed of light.

Calculation of amplitude of electric field in EM wave in vacuum

Using

$I = \frac{1}{2} ε_{0} c E_{^{m a x^{2}}}$

$E_{m a x} = \frac{2 I}{ε_{0} c}$

Put the values of constants in above equation

$E_{\max} = \sqrt{\frac{2 (5.04 \times 10^{5} W / m^{2})}{8.85 \times 10^{- 12} C^{2} N . m^{2} (3 \times 10^{8} m / s)}} E_{\max} = 1.95 \times 10^{4} V / m$

Thus, the amplitude of the electric field of the electromagnetic radiation is

1.95 \times 10^{4} V / m

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A laser beam has diameter 1.20 mm. What is the amplitude of the electric field of the electromagnetic radiation in this beam if the beam exerts a force of $3.8 \times 10^{- 9} N$ on a totally reflecting surface?

Short Answer

Step by step solution

Radiation pressure exerted by electromagnetic wave

Calculation of amplitude of electric field in EM wave in vacuum

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A laser beam has diameter 1.20 mm. What is the amplitude of the electric field of the electromagnetic radiation in this beam if the beam exerts a force of 3.8×10-9Non a totally reflecting surface?

Short Answer

Step by step solution

Radiation pressure exerted by electromagnetic wave

Calculation of amplitude of electric field in EM wave in vacuum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Modern Physics

Atoms and Radioactivity

Measurements

Waves Physics

Fundamentals of Physics

Conservation of Energy and Momentum

Study anywhere. Anytime. Across all devices.

A laser beam has diameter 1.20 mm. What is the amplitude of the electric field of the electromagnetic radiation in this beam if the beam exerts a force of $3.8 \times 10^{- 9} N$ on a totally reflecting surface?