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Electromagnetic radiation: oscillating electric and magnetic fields propagate outward from a source at the speed of light. The fields E and B remain mutually perpendicular and orthogonal to the radial unit vector r̂. Intensity I of the radiation decreases with the inverse square of the distance, I ∝ r⁻².

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Matheorems

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13,498 görüntüleme • 18 gün önce •via X (Twitter)

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An electric dipole p(t) = p₀ sin(ωt) ẑ oscillating at a point radiates a field that, far away, falls off only as 1/r. Its radiation term is E = (μ₀/4π) p̈(t − r/c) sin θ / r along θ̂, with B = r̂ × E / c along φ̂, so E, B and the direction of travel r̂ are mutually perpendicular. The intensity goes as sin²θ / r²: zero along the axis, strongest at the equator. Every sphere around the source carries the same mean power, p₀²ω⁴ / (12πε₀c³).
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An electric dipole p(t) = p₀ sin(ωt) ẑ oscillating at a point radiates a field that, far away, falls off only as 1/r. Its radiation term is E = (μ₀/4π) p̈(t − r/c) sin θ / r along θ̂, with B = r̂ × E / c along φ̂, so E, B and the direction of travel r̂ are mutually perpendicular. The intensity goes as sin²θ / r²: zero along the axis, strongest at the equator. Every sphere around the source carries the same mean power, p₀²ω⁴ / (12πε₀c³).

matharium

91,162 görüntüleme • 15 gün önce

One of my studies on electromagnetic sculpting from a couple of years ago. Exploring magnetic fields and the emergent interaction between matter and electricity.
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One of my studies on electromagnetic sculpting from a couple of years ago. Exploring magnetic fields and the emergent interaction between matter and electricity.

maxim zhestkov

75,868 görüntüleme • 10 ay önce

The Physics of Moving Charges and Magnetic Fields 🧲✨
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The Physics of Moving Charges and Magnetic Fields 🧲✨

Real World Physics

12,249 görüntüleme • 4 ay önce

At the heart of our Milky Way lies Sagittarius A*, the supermassive black hole with a mass of about 4.3 million suns. Recent observations from the Event Horizon Telescope have revealed something remarkable: the magnetic fields surrounding it are not the turbulent, disordered chaos scientists once expected, but instead form a strong, coherent spiral structure.These organized, twisted magnetic fields thread through the swirling hot plasma near the event horizon, acting like invisible guides that regulate how matter flows inward. They help control the acceleration and heating of gas, determine the intensity of emitted radiation, and stabilize the chaotic environment just outside the point of no return.This discovery, achieved by imaging polarized light from the accretion disk, shows striking similarities to the magnetic geometry seen around the much larger black hole in M87—despite vast differences in size and activity level. It suggests that powerful, ordered magnetic fields are a universal feature of supermassive black holes, playing a central role in how they feed, influence their surroundings, and potentially launch jets.The findings deepen our understanding of extreme plasma physics under intense gravity, test general relativity in its strongest regime, and highlight the profound interplay between magnetic forces and spacetime itself. Even in our relatively quiet galactic center, these fields reveal a hidden capacity for dynamic, powerful behavior—reminding us that black holes are not just gravitational sinks, but complex engines shaped by electromagnetism on cosmic scales.Future observations promise even sharper views and time-lapse sequences, offering deeper insights into the fundamental processes driving the hearts of galaxies.
0:15

At the heart of our Milky Way lies Sagittarius A*, the supermassive black hole with a mass of about 4.3 million suns. Recent observations from the Event Horizon Telescope have revealed something remarkable: the magnetic fields surrounding it are not the turbulent, disordered chaos scientists once expected, but instead form a strong, coherent spiral structure.These organized, twisted magnetic fields thread through the swirling hot plasma near the event horizon, acting like invisible guides that regulate how matter flows inward. They help control the acceleration and heating of gas, determine the intensity of emitted radiation, and stabilize the chaotic environment just outside the point of no return.This discovery, achieved by imaging polarized light from the accretion disk, shows striking similarities to the magnetic geometry seen around the much larger black hole in M87—despite vast differences in size and activity level. It suggests that powerful, ordered magnetic fields are a universal feature of supermassive black holes, playing a central role in how they feed, influence their surroundings, and potentially launch jets.The findings deepen our understanding of extreme plasma physics under intense gravity, test general relativity in its strongest regime, and highlight the profound interplay between magnetic forces and spacetime itself. Even in our relatively quiet galactic center, these fields reveal a hidden capacity for dynamic, powerful behavior—reminding us that black holes are not just gravitational sinks, but complex engines shaped by electromagnetism on cosmic scales.Future observations promise even sharper views and time-lapse sequences, offering deeper insights into the fundamental processes driving the hearts of galaxies.

Black Hole

30,841 görüntüleme • 9 ay önce

NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions paper page: present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.
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NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions paper page: present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

AK

194,523 görüntüleme • 3 yıl önce

When a nuclear reactor is switched on for the first time, an intense, almost hypnotic blue glow appears in the water surrounding the reactor core. This light is neither fire nor heat; it is Cherenkov radiation, a physical phenomenon that occurs when charged particles, such as high-energy electrons produced during nuclear fission, travel through a transparent medium faster than light can propagate within that same medium. While nothing can exceed the speed of light in a vacuum, light travels more slowly in materials like water. When a charged particle surpasses this reduced speed, it emits a coherent shock-like electromagnetic wave, often described as an optical analogue of a sonic boom. This radiation produces the distinctive blue glow. The colour arises because Cherenkov radiation is strongest at shorter wavelengths, which are dominated by blue and ultraviolet light. The phenomenon was first observed experimentally in 1934 and later explained theoretically, work that led to the Nobel Prize in Physics in 1958. Its explanation confirmed how relativity and electromagnetism operate in material media. Today, this deep blue light is both a warning and a scientific tool. It signals the presence of intense ionising radiation, while also being exploited in particle detectors, nuclear reactors, and neutrino observatories. It provides a rare, visible manifestation of subatomic processes that are otherwise hidden from direct human perception. #GottaLovePhysics #Physics
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When a nuclear reactor is switched on for the first time, an intense, almost hypnotic blue glow appears in the water surrounding the reactor core. This light is neither fire nor heat; it is Cherenkov radiation, a physical phenomenon that occurs when charged particles, such as high-energy electrons produced during nuclear fission, travel through a transparent medium faster than light can propagate within that same medium. While nothing can exceed the speed of light in a vacuum, light travels more slowly in materials like water. When a charged particle surpasses this reduced speed, it emits a coherent shock-like electromagnetic wave, often described as an optical analogue of a sonic boom. This radiation produces the distinctive blue glow. The colour arises because Cherenkov radiation is strongest at shorter wavelengths, which are dominated by blue and ultraviolet light. The phenomenon was first observed experimentally in 1934 and later explained theoretically, work that led to the Nobel Prize in Physics in 1958. Its explanation confirmed how relativity and electromagnetism operate in material media. Today, this deep blue light is both a warning and a scientific tool. It signals the presence of intense ionising radiation, while also being exploited in particle detectors, nuclear reactors, and neutrino observatories. It provides a rare, visible manifestation of subatomic processes that are otherwise hidden from direct human perception. #GottaLovePhysics #Physics

Erika 

280,571 görüntüleme • 9 ay önce

The self-sculpting force of a magnetic storm. A piece from my explorations of energy and its electromagnetic beauty.
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The self-sculpting force of a magnetic storm. A piece from my explorations of energy and its electromagnetic beauty.

maxim zhestkov

35,659 görüntüleme • 10 ay önce

R&B with the intensity of rock. The penmanship of hip-hop. And a boom that's going to shake the world. Meet Mr.Mrs and watch his exclusive #UpNext mini doc:
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R&B with the intensity of rock. The penmanship of hip-hop. And a boom that's going to shake the world. Meet Mr.Mrs and watch his exclusive #UpNext mini doc:

Apple Music

1,005,022 görüntüleme • 2 yıl önce

A turnstile antenna is two crossed dipoles driven 90° apart, one dipole p turning at ω about its mast. Its far field E ∝ r̂ × (r̂ × p̈(t − r/c)) has phase ωt − kr − φ at every latitude, so each wavefront is the spiral r = (ωt − φ − 2πn)/k. Along the mast E ∝ (1/r)[cos(kr − ωt) ŷ + sin(kr − ωt) x̂] keeps its length and turns once per period, and B = (1/c) r̂ × E turns with it. In the plane of the cross the same wave is linearly polarized.
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A turnstile antenna is two crossed dipoles driven 90° apart, one dipole p turning at ω about its mast. Its far field E ∝ r̂ × (r̂ × p̈(t − r/c)) has phase ωt − kr − φ at every latitude, so each wavefront is the spiral r = (ωt − φ − 2πn)/k. Along the mast E ∝ (1/r)[cos(kr − ωt) ŷ + sin(kr − ωt) x̂] keeps its length and turns once per period, and B = (1/c) r̂ × E turns with it. In the plane of the cross the same wave is linearly polarized.

matharium

81,717 görüntüleme • 9 gün önce

The Earth's magnetic field protects us not only from solar flares but also from cosmic radiation. When the Sun enters a Grand Solar Minimum, its magnetic field weakens for a long period. This lets more cosmic radiation into the Solar System, and this directly impacts the climate on Earth and increases volcanic activity. The last Little Ice Age occurred during a Grand Solar Minimum. But the coming Grand Solar Minimum is going to hit harder because the Earth's magnetic field is at least 30% weaker and, with the ongoing geomagnetic excursion, is continuing to weaken. This will let in more cosmic radiation, which will directly cause mutations, pandemics, cooling, crop failures, and even crustal displacement. Since the advent of modern technology, we haven't experienced either a Grand Solar Minimum or a geomagnetic excursion, and we are due for both.
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The Earth's magnetic field protects us not only from solar flares but also from cosmic radiation. When the Sun enters a Grand Solar Minimum, its magnetic field weakens for a long period. This lets more cosmic radiation into the Solar System, and this directly impacts the climate on Earth and increases volcanic activity. The last Little Ice Age occurred during a Grand Solar Minimum. But the coming Grand Solar Minimum is going to hit harder because the Earth's magnetic field is at least 30% weaker and, with the ongoing geomagnetic excursion, is continuing to weaken. This will let in more cosmic radiation, which will directly cause mutations, pandemics, cooling, crop failures, and even crustal displacement. Since the advent of modern technology, we haven't experienced either a Grand Solar Minimum or a geomagnetic excursion, and we are due for both.

Open Minded Approach

92,374 görüntüleme • 3 ay önce

42,000 years ago, during the Laschamp Geomagnetic Excursion, there was an abrupt climate change event in which the Neanderthals went extinct and humans barely survived. One study links this abrupt climate change to increased cosmic radiation caused by a weakened magnetic field and Grand Solar Minima. The speed of the pole shift measured during the Laschamp Excursion is very close to the acceleration of the North Magnetic Pole observed in the 1990s. The same thing is happening today.
0:10

42,000 years ago, during the Laschamp Geomagnetic Excursion, there was an abrupt climate change event in which the Neanderthals went extinct and humans barely survived. One study links this abrupt climate change to increased cosmic radiation caused by a weakened magnetic field and Grand Solar Minima. The speed of the pole shift measured during the Laschamp Excursion is very close to the acceleration of the North Magnetic Pole observed in the 1990s. The same thing is happening today.

Open Minded Approach

77,637 görüntüleme • 4 ay önce

During a Grand Solar Minimum and a geomagnetic excursion, Earth becomes the dangerous place. A weak magnetic field means unstable radiation belts, ionospheric chaos, satellite failure, GPS collapse, and increased cosmic radiation at the surface. The Moon doesn’t suffer from this chaos. It has no magnetosphere to collapse, no ionosphere to destabilize, and radiation in deep space is harsh but stable and predictable. With just a few meters of lunar regolith, underground bases on the Moon, especially on the far side, become better shielded, more reliable, and more survivable than Earth orbit or even Earth’s surface. That’s why the Moon isn’t a distraction. It’s the logical place to ride out what’s coming.
0:12

During a Grand Solar Minimum and a geomagnetic excursion, Earth becomes the dangerous place. A weak magnetic field means unstable radiation belts, ionospheric chaos, satellite failure, GPS collapse, and increased cosmic radiation at the surface. The Moon doesn’t suffer from this chaos. It has no magnetosphere to collapse, no ionosphere to destabilize, and radiation in deep space is harsh but stable and predictable. With just a few meters of lunar regolith, underground bases on the Moon, especially on the far side, become better shielded, more reliable, and more survivable than Earth orbit or even Earth’s surface. That’s why the Moon isn’t a distraction. It’s the logical place to ride out what’s coming.

Open Minded Approach

31,564 görüntüleme • 8 ay önce

Dozens of protestors here at Lincoln’s Inn Fields covering their faces with masks and no arrests from the police…
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Dozens of protestors here at Lincoln’s Inn Fields covering their faces with masks and no arrests from the police…

Dov Forman

239,481 görüntüleme • 5 gün önce

The Ghost of Cassiopeia: a cosmic phantom in the glow of a volatile star 👻 Located 550 light-years from Earth, the IC 63 nebula is a ghostly cloud of dust and gas. It is gradually being eroded by the intense radiation from a nearby, unpredictable star: Gamma Cassiopeiae. Autumn and winter are the best times to observe this remarkable object from the Northern Hemisphere. 🔭
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The Ghost of Cassiopeia: a cosmic phantom in the glow of a volatile star 👻 Located 550 light-years from Earth, the IC 63 nebula is a ghostly cloud of dust and gas. It is gradually being eroded by the intense radiation from a nearby, unpredictable star: Gamma Cassiopeiae. Autumn and winter are the best times to observe this remarkable object from the Northern Hemisphere. 🔭

Black Hole

24,114 görüntüleme • 2 ay önce

One of the main indicators that the Earth's magnetic field is weakening is that the auroras are visible at lower latitudes. The main fear of the elites is that, during a Grand Solar Minimum and increased cosmic radiation, the entire climate, food chain, and global system will collapse. Most of them don't expect crustal displacement and the floods, but they are building doomsday bunkers with separate power grids and supplies that will last them for generations. The higher elites, however, build doomsday bunkers in special locations with higher magnetic anomalies, and I have revealed most of those places to my subscribers, but there's more, so stay tuned.
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One of the main indicators that the Earth's magnetic field is weakening is that the auroras are visible at lower latitudes. The main fear of the elites is that, during a Grand Solar Minimum and increased cosmic radiation, the entire climate, food chain, and global system will collapse. Most of them don't expect crustal displacement and the floods, but they are building doomsday bunkers with separate power grids and supplies that will last them for generations. The higher elites, however, build doomsday bunkers in special locations with higher magnetic anomalies, and I have revealed most of those places to my subscribers, but there's more, so stay tuned.

Open Minded Approach

90,758 görüntüleme • 3 ay önce