The electric component of a beam of polarized light is Ey=(5.00 V / m) sin[(1.00 ×10^6 m^-1) z

step 1 In this question, we are given the electric field components of a polarized light. So EY is equa

The electric component of a beam of polarized light is...

The electric component of a beam of polarized light is $$ E_{y}=(5.00 \mathrm{~V} / \mathrm{m}) \sin \left[\left(1.00 \times 10^{6} \mathrm{~m}^{-1}\right) z+\omega t\right] $$ (a) Write an expression for the magnetic field component of the wave, including a value for $\omega .$ What are the (b) wavelength, (c) period, and (d) intensity of this light? (e) Parallel to which axis does the magnetic field oscillate? (f) In which region of the electromagnetic spectrum is this wave?

The electric component of a beam of polarized light is
$$
E_{y}=(5.00 \mathrm{~V} / \mathrm{m}) \sin \left[\left(1.00 \times 10^{6} \mathrm{~m}^{-1}\right) z+\omega t\right]
$$
(a) Write an expression for the magnetic field component of the wave, including a value for $\omega .$ What are the (b) wavelength,
(c) period, and (d) intensity of this light? (e) Parallel to which axis does the magnetic field oscillate? (f) In which region of the electromagnetic spectrum is this wave?

Key Concepts

Electromagnetic Spectrum

The electromagnetic spectrum is the complete range of electromagnetic radiation, from radio waves with very long wavelengths to gamma rays with very short wavelengths. The classification of a particular wave within this spectrum depends on its wavelength or frequency, and it determines the wave's interaction with matter, facilitating various applications such as telecommunications, medical imaging, and astronomical observations.

Polarization of Light

Polarization describes the orientation of the electric field oscillations in an electromagnetic wave. In a polarized beam, the electric field oscillates in a single plane, which in turn determines the orientation of the magnetic field oscillations. Polarization is a key property in many optical applications, affecting how light interacts with materials and how it can be manipulated using polarizing filters.

Intensity of Electromagnetic Waves

Intensity in the context of electromagnetic waves refers to the power transmitted per unit area, which is directly related to the square of the amplitude of the electric field. It is typically calculated using formulas that involve the permittivity of free space and the speed of light. This concept describes how energy is distributed in the wave and is essential for understanding the energy transfer associated with different forms of electromagnetic radiation.

Wave Parameters (Wavelength, Frequency, and Period)

The wavelength, frequency, and period are fundamental parameters that describe any oscillatory motion, including electromagnetic waves. The wavelength is the spatial period of the wave, the frequency is the number of oscillations per unit time, and the period is the reciprocal of the frequency. These parameters are linked by the relation c = ??, where c is the speed of light, ensuring consistency between spatial and temporal variations in the wave.

Relationship Between Electric and Magnetic Fields

In an electromagnetic wave, the electric and magnetic fields are perpendicular to each other and to the direction of wave propagation. Their amplitudes are related by the speed of light, typically expressed as B = E/c in SI units. This relation is crucial for determining one field component if the other is known and for ensuring that the wave complies with the constraints set by Maxwell’s equations.

Electromagnetic Waves

Electromagnetic waves are propagating disturbances in the electric and magnetic fields that travel through space at the speed of light. They are solutions to Maxwell's equations, which demonstrate that time-varying electric fields generate magnetic fields and vice versa. This interdependent oscillation allows the energy to propagate without the need for a material medium.

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