Hidden Supersymmetry of Electrostatic Fields

Juan D. García-Muñoz, A Raya

A hidden supersymmetry of electrostatic fields is evidenced. Proposing an ansatz for the electrostatic potential as the natural logarithm of a nodeless function, it is demonstrated that the electrostatic fields fulfil the Bernoulli equation associated to a second-order confluent supersymmetric transformation. By using the so-called confluent algorithm, it is possible, through the appropriate choice of a charge density, to find the ground state of the corresponding supersymmetric initial potential. Furthermore, the associated electrostatic field profile of a Schr{ö}dinger-like solvable potentials can be determined

read more at https://arxiv.org/pdf/2209.01248.pdf

What causes rare rainbow arcs?

The nature of polarized light using smartphones

Martín Monteiro, Cecilia Stari, Cecilia Cabeza, Arturo C. Marti

Originally an empirical law, nowadays Malus’ is seen as a key experiment to demonstrate the traversal nature of electromagnetic waves, as well as the intrinsic connection between optics and electromagnetism. More specifically, it is an operational way to characterize a linear polarized electromagnetic wave. A simple and inexpensive setup is proposed in this work, to quantitatively verify the nature of polarized light. A flat computer screen serves as a source of linear polarized light and a smartphone is used as a measuring instrument thanks to its built-in sensors. The intensity of light is measured by means of the luminosity sensor with a tiny filter attached over it. The angle between the plane of polarization of the source and the filter is measured by means of the three-axis accelerometer, that works, in this case, as an incliometer. Taken advantage of the simultaneous use of these two sensors, a complete set of measures can be obtained just in a few seconds. The experimental light intensity as a function of the angle shows an excellent agreement with standard results…
…. Read more at https://arxiv.org/ftp/arxiv/papers/1607/1607.02659.pdf

Magnetic Putty Time Lapse

Magnetic putty time lapse as it absorbs a rare-earth magnet. Taken over 1.5 hours at 3fps, played back at 24fps. The magnetic putty will eventually arrange itself so that the outer surface is as evenly distributed around the magnet as possible.

Ferromagnetic particles in the putty are strongly attracted to the magnet and very slowly engulf the surface of the magnet. The magnet shown in the picture is a strong neodymium iron boron magnet. It’s a very powerful magnet for its size and could erase magnetic stripes found in credit cards and damage electronics!

The putty looks and feels like regular silly putty, but the difference lies in the fact that it has been infused with millions of micron-sized ferrous particles (most often iron oxide powder). The magnetic putty is not actually magnetic by itself, since the infused particles are made of iron powder.

The presence of the strong neodymium iron boron magnet (the silver cube in the video) magnetizes the ferromagnetic particles in the putty. When this happens, the ferrous particles align with each other and this alignment generates north and south magnetic poles, making the putty into a temporary magnet. Once magnetized, the putty will remain magnetized even after the rare-earth magnet has been removed from the putty. This effect persists for a few hours until thermal agitation shakes the particles and they lose their alignment.

A Penny For Your Thoughts

How much is your time really worth? Student paper evaluates the economics of thought

Big thinkers may wish to re-evaluate their rates, according to a student study at the University of Leicester, which tested the popular idiom ‘A penny for your thoughts’ by working out how much of a person’s thought could theoretically be purchased with a single penny.

The study suggests that a penny could, in theory, purchase 3 hours, 7 minutes and 30 seconds of thought according to Natural Sciences student Osarenkhoe Uwuigbe from the University of Leicester’s Centre for Interdisciplinary Science.
In a paper published in the Journal of Interdisciplinary Science Topics, a peer-reviewed student journal run by the University of Leicester’s Centre for Interdisciplinary Science, the student first investigated how much power is needed to produce thought.
For simplicity, the study examined the power necessary for the brain – which consumes roughly 20 per cent of the body’s energy – to run as being the power necessary for the production of thought.
Given that the average power consumption of a typical adult is approximately 100 watts, the student calculated that the power necessary to run a human brain and produce thought is roughly 20 per cent of this – or 20 watts.
To apply monetary value to thought, the price per kilowatt hour (kWh) charged by UK energy companies was calculated, settling on 16 pence per kWh, which is within the range of prices typically charged by UK energy companies.
Assuming that it requires 20 W or 1/50 kW to produce thought, charging 16p per kWh means that one penny can purchase 1/16th of a kWh. Therefore the length of time (in hours) a penny can purchase thought for is (1/16)÷(1/50)=3.125.
Assuming that it is possible to think as fast as you can speak, the student suggests that 3 hours, 7 minutes and 30 seconds of thought and speech can be bought with a penny.
Student Osarenkhoe Uwuigbe said: “This model is likely to be an underestimate as power required for the brain to operate does not necessarily translate to power used in thought. The brain has several autonomic functions it carries out during thought processing and as a result thought processing could not take 100% of the power consumption of the brain.
“Furthermore, it is unlikely that it is possible to think as fast as you speak due to delay caused by biological constrains such as conduction velocity of nerves carrying the signal from the brain to the mouth, the release of Ca²⁺ ions during muscle contraction of the tongue and lips and so on.”
Dr Cheryl Hurkett from the University of Leicester’s Centre for Interdisciplinary Science said: “An important part of being a professional scientist (as well as many other professions) is the ability to make connections between the vast quantity of information students have at their command, and being able to utilise the knowledge and techniques they have previously mastered in a new or novel context.
“The Interdisciplinary Research Journal module models this process, and gives students an opportunity to practise this way of thinking. The intention of this module is to allow students to experience what it’s like to be at the cutting edge of scientific research.
“The course is engaging to students and the publishing process provides them with an invaluable insight into academic publishing. It also helps students feel more confident when submitting future papers. I find it a very rewarding module to teach and I am always pleased to see my students engaging so enthusiastically with the subject. I encourage them to be as creative as possible with their subject choices as long as they can back it up with hard scientific facts, theories and calculations!”

Read more at: phys.org – physics.le.ac.uk

Tracking the radiation reaction energy when charged bodies accelerate

Andrew M. Steane – scitation.aip.org
We consider radiation reaction and energy conservation in classical electromagnetism. We first treat the well-known problem of energy accounting during radiation from a uniformly accelerating particle. This gives rise to the following paradox: when the self-force vanishes, the system providing the applied force does only enough work to give the particle its kinetic energy—so where does the energy that is eventually radiated away come from? We answer this question using a modern treatment of radiation reaction and self-force, as it appears in the expression due to Eliezer and Ford and O’Connell. We clarify the influence of the Schott force, and we find that the radiated power is , which differs from Larmor’s formula. Finally, we present a simple and highly visual argument that enables one to track the radiated energy without the need to appeal to the far field in the distant future (the “wave zone”)…
Read more at http://arxiv.org/pdf/1408.1349v1.pdf

On equivalent resistance of electrical circuits

Mikhail Kagan
While the standard (introductory physics) way of computing the equvalent resistance of non-trivial electrical ciruits is based on Kirchhoff’s rules, there is a mathematically and conceptually simpler approach, called the method of nodal potentials, whose basic variables are the values of electric potential at the circuit’s nodes.
In this paper, we review the method of nodal potentials and illustrate it using the Wheatstone bridge as an example. At the end, we derive – in a closed form – the equivalent resistance of a generic circuit, which we apply to a few sample circuits. The final result unveils a curious interplay between electrical circuits, matrix algebra, and graph theory and its applications to computer science. The paper is written at a level accessible by undergraduate students who are familiar with matrix arithmetic. For the more inquisitive reader, additional proofs and technical details are provided in the appendix.
Read more at http://arxiv.org/pdf/1507.01873v1.pdf

Tesla vs. Edison: A Mythical Rivalry

Nikola Tesla with his coil in 1896. Credits: Electrical Review

The figure of the mad scientist, the eccentric genius, no longer belongs exclusively to Einstein. In the last two decades, the public fascination with the figure of Nikola Tesla has enlarged the myth to such an extent that it now exceeds the unquestionable achievements of this great Serbian inventor. In popular culture, Tesla is seen as an unsung hero whose merits were not sufficiently recognized. And in this mythical story appears a greedy villain named Thomas Edison, who first does his best to prevent Tesla’s success and later tries to smother his recognition …
… Read more at www.bbvaopenmind.com