Barrow, in his 2020 paper 'Non-Euclidean Newtonian Cosmology,' elaborates on the behavior of force (F) and potential (Φ) within hyperbolic 3-space (H3). The inherent curvature in these spaces impacts physical laws, underpinning various fields such as cosmology, general relativity, and string theory. The inverse-square law, fundamental in Euclidean spaces, also applies to non-Euclidean geometries, including hyperbolic space. Given that the space outside the source is divergence free. Intensity 1 × distance 1 2 = intensity 2 × distance 2 2 The intensity is proportional (see ∝) to the reciprocal of the square of the distance thus: In mathematical notation the inverse square law can be expressed as an intensity (I) varying as a function of distance (d) from some centre. To prevent dilution of energy while propagating a signal, certain methods can be used such as a waveguide, which acts like a canal does for water, or how a gun barrel restricts hot gas expansion to one dimension in order to prevent loss of energy transfer to a bullet. Radar energy expands during both the signal transmission and the reflected return, so the inverse square for both paths means that the radar will receive energy according to the inverse fourth power of the range. The fundamental cause for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space. In science, an inverse-square law is any scientific law stating that the observed 'intensity' of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. Thus the field intensity is inversely proportional to the square of the distance from the source. The density of flux lines is inversely proportional to the square of the distance from the source because the surface area of a sphere increases with the square of the radius. The total number of flux lines depends on the strength of the light source and is constant with increasing distance, where a greater density of flux lines (lines per unit area) means a stronger energy field. The lines represent the flux emanating from the sources and fluxes. S represents the light source, while r represents the measured points. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This hypothesis was based on the assumption that light traveled purely as a wave through space. This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. To explain the photoelectric effect, 19th-century physicists theorized that the oscillating electric field of the incoming light wave was heating the electrons and causing them to vibrate, eventually freeing them from the metal surface. The wave energy is determined by the wave amplitude. In electromagnetic waves, the amplitude is the maximum field strength of the electric and magnetic fields ( Figure 16.10). If some energy is later absorbed, the field strengths are diminished and anything left travels on.Ĭlearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries. Once created, the fields carry energy away from a source. However, there is energy in an electromagnetic wave itself, whether it is absorbed or not. These fields can exert forces and move charges in the system and, thus, do work on them. Other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells.Įlectromagnetic waves bring energy into a system by virtue of their electric and magnetic fields. Sometimes this energy is obvious, such as in the warmth of the summer Sun. Explain how the energy of an electromagnetic wave depends on its amplitude, whereas the energy of a photon is proportional to its frequencyĪnyone who has used a microwave oven knows there is energy in electromagnetic waves.Calculate the Poynting vector and the energy intensity of electromagnetic waves.Express the time-averaged energy density of electromagnetic waves in terms of their electric and magnetic field amplitudes.

By the end of this section, you will be able to:

Equation for intensity fo light