Glossary

24.4 Energy in Electromagnetic Waves

3 min read•june 18, 2024

transfer energy through oscillating . These waves carry energy proportional to their frequency, with higher frequency waves transferring energy more efficiently. Understanding this concept is crucial for grasping how electromagnetic radiation interacts with matter.

, a key measure of electromagnetic wave energy, is calculated using electric or strengths. This relationship between field strength and energy transfer helps explain phenomena like sunburns from UV light and the penetrating power of in medical imaging.

Energy Transfer in Electromagnetic Waves

Energy transfer in electromagnetic waves

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  • transfer energy through oscillating electric and magnetic fields perpendicular to each other and the direction
    • oscillations accelerate charges back and forth (electrons in an antenna)
    • Magnetic field oscillations induce electric currents (in a receiving antenna)
  • Energy transfers via propagation of these oscillating fields
    • Electric field component exerts forces on charged particles transferring energy
    • Magnetic field component induces electric currents transferring energy
  • of an electromagnetic wave is proportional to the square of electric and magnetic field amplitudes
    • Energy density quantifies energy per unit volume
    • Higher field amplitudes yield higher energy densities (more intense waves)
  • The describes the direction and magnitude of electromagnetic energy flow

Intensity calculation of electromagnetic waves

  • is power per unit area carried by an electromagnetic wave
    • Power is energy transfer rate
    • Area is perpendicular to wave propagation direction
  • Intensity (II) relates to electric field strength (EE) by: I=12ϵ0cE2I = \frac{1}{2} \epsilon_0 c E^2
    • ϵ0\epsilon_0 is of free space
    • cc is speed of light
  • Intensity also expressed using magnetic field strength (BB): I=12μ0B2I = \frac{1}{2 \mu_0} B^2
    • μ0\mu_0 is
  • To calculate intensity, measure peak electric or magnetic field strength and substitute into appropriate equation (using EE or BB)

Frequency vs energy transfer efficiency

  • Energy carried by an electromagnetic wave is directly proportional to its frequency
    • Higher frequency waves have higher energy photons ()
    • Lower frequency waves have lower energy photons ()
  • Photon energy (EE) given by: E=hfE = hf
    • hh is
    • ff is electromagnetic wave frequency
  • Higher frequency waves transfer energy more efficiently than lower frequency waves
    • More energy transferred per photon at higher frequencies
    • Given intensity of high-frequency waves carries more energy than same intensity low-frequency waves (ultraviolet vs visible light)
  • Examples:
    • (high frequency) more penetrating and damaging to biological tissue than (low frequency) at same intensity
    • (high frequency) causes sunburn and skin damage more readily than visible light (lower frequency) at same intensity
    • X-rays (high frequency) used for medical imaging due to ability to pass through soft tissues while being absorbed by denser bone

Additional Electromagnetic Wave Properties

  • describes the orientation of electric field oscillations in an electromagnetic wave
  • The categorizes waves based on their frequencies and wavelengths, from radio waves to gamma rays
  • explains how electromagnetic radiation can exhibit both wave-like and particle-like properties

Key Terms to Review (26)

Amplitude: Amplitude is the maximum displacement of a wave or oscillating object from its equilibrium position. It measures the extent of change in the wave's physical quantity such as height or pressure.
Direction of polarization: Direction of polarization refers to the orientation of the electric field vector in an electromagnetic wave. It describes how the electric field oscillates as the wave propagates.
Electric and magnetic fields: Electric and magnetic fields are two interdependent fields that propagate as waves through space. They form the basis of electromagnetic waves, where oscillations in one field induce oscillations in the other.
Electric Field: The electric field is a vector field that describes the force experienced by a stationary, positive test charge at any given point in space. It represents the strength and direction of the electric force exerted on a charged particle by other charges in the vicinity, and is a fundamental concept in the study of electromagnetism and the behavior of charged particles.
Electromagnetic spectrum: The electromagnetic spectrum is the range of all types of electromagnetic radiation, which includes visible light, radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays. This spectrum is crucial because it encompasses the various forms of energy that travel through space at the speed of light and affects many aspects of physics, including radiation, magnetism, wave production, and energy transfer.
Electromagnetic waves: Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space. They travel at the speed of light and do not require a medium.
Electromagnetic Waves: Electromagnetic waves are a form of energy that propagates through space and time as oscillating electric and magnetic fields. These waves are capable of transmitting energy without the need for a physical medium, and they can travel at the speed of light.
Energy Density: Energy density is a measure of the amount of energy stored per unit volume or mass of a substance. It is an important concept in various fields, including energy production, transportation, and storage, as it determines the efficiency and capacity of energy systems.
Gamma rays: Gamma rays are a form of electromagnetic radiation with the highest photon energies and shortest wavelengths. They are typically produced by nuclear reactions, radioactive decay, and certain types of astronomical phenomena.
Gamma Rays: Gamma rays are a type of high-energy electromagnetic radiation with the shortest wavelength and highest frequency in the electromagnetic spectrum. They are produced by the radioactive decay of atomic nuclei and have the ability to penetrate deep into matter, making them useful in various applications.
Intensity: Intensity is the power per unit area carried by a wave, typically measured in watts per square meter ($W/m^2$). It quantifies the energy flow through a given surface area perpendicular to the direction of wave propagation.
Intensity: Intensity is a measure of the amount of energy or power transmitted through a given area per unit of time. It is a fundamental concept that describes the strength or magnitude of a physical quantity, such as a wave, field, or radiation, and is crucial in understanding various phenomena in physics.
Magnetic Field: A magnetic field is a region in space where magnetic forces can be detected. It is a vector field that describes the magnetic influence of electric currents and magnetized materials on the space around them. The magnetic field is a fundamental concept in electromagnetism and is essential for understanding various phenomena in physics, including the behavior of ferromagnets, the motion of charged particles, and the production of electromagnetic waves.
Maximum field strength: Maximum field strength is the peak value of the electric or magnetic field in an electromagnetic wave. It represents the highest intensity of the field at any point in time.
Permeability: Permeability is a measure of the ability of a material to allow the passage of a fluid, such as a magnetic field, through it. It is a fundamental property that describes the ease with which a material can be magnetized or demagnetized, and it plays a crucial role in understanding electromagnetic phenomena like eddy currents and the propagation of electromagnetic waves.
Permeability of free space: Permeability of free space, denoted as $\mu_0$, is a physical constant that describes how magnetic fields interact with the vacuum. It is essential in calculating the strength of magnetic fields generated by currents.
Permittivity: Permittivity is a measure of the ability of a material to store electric energy in an electric field. It is a fundamental property that describes how an electric field affects, and is affected by, a dielectric medium. Permittivity is a crucial concept in understanding the behavior of electric fields, energy storage in capacitors, and the propagation of electromagnetic waves.
Planck's constant: Planck's constant is a fundamental physical constant that represents the smallest possible change in energy or action. It is a crucial parameter in quantum mechanics and is denoted by the symbol 'h'. Planck's constant establishes the relationship between the energy of a photon and its frequency, and it is a key factor in understanding the quantization of energy and the wave-particle duality of matter and energy.
Polarization: Polarization is a fundamental property of electromagnetic waves, including light, that describes the orientation of the electric field oscillations within the wave. It is a crucial concept that underlies many important phenomena in the fields of static electricity, electromagnetism, and optics.
Poynting Vector: The Poynting vector is a mathematical quantity that describes the directional energy flux (the flow of energy per unit area) of an electromagnetic field. It represents the rate of energy transfer per unit area of an electromagnetic wave.
Radio waves: Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. They have frequencies ranging from about 3 kHz to 300 GHz.
Radio Waves: Radio waves are a type of electromagnetic radiation with wavelengths in the range of about 1 millimeter to 100 kilometers, and frequencies between 3 kilohertz to 300 gigahertz. They are used for various applications, including radio and television broadcasting, wireless communication, and radar detection.
Ultraviolet Light: Ultraviolet (UV) light is a type of electromagnetic radiation with wavelengths shorter than visible light, but longer than X-rays. It is a high-energy form of light that can have both beneficial and harmful effects on living organisms and materials.
Wave Propagation: Wave propagation refers to the movement and transmission of waves through a medium or space. It describes how waves, such as electromagnetic waves or sound waves, travel and spread out from their source, transferring energy without the movement of the medium itself.
Wave-Particle Duality: Wave-particle duality is a fundamental concept in quantum physics that describes the dual nature of light and matter, where they exhibit characteristics of both waves and particles depending on the context and experimental conditions. This principle is central to understanding the behavior of electromagnetic radiation and the properties of subatomic particles.
X-rays: X-rays are a form of electromagnetic radiation with very short wavelengths, typically ranging from 0.01 to 10 nanometers. They are widely used in various applications, particularly in medical imaging and treatments, due to their ability to penetrate soft tissues while being absorbed by denser materials like bones.
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