Expert Math and Science Articles

electric potential

Introduction to Electric Vector Potential and Its Applications

/16 Comments/in /by

Main Point: The electric vector potential offers a  means of determining the non-conservative component of a mixed stationary or quasi-stationary electric field While many are familiar with the static magnetic vector potential ## \bf A = (\mu/4\pi) \int \bf j~ dv/s ## with ## \bf j ## = current (area) density within differential volume ##…

Trending Articles

Recent Entries

Learn the Math

I Know the Math Says so, but Is It Really True?

64 Comments
/
I'm sure anyone who has hung out long enough here on Physics Forums has encountered threads which go something like this (I'll use an example based on…
block universe time illusion

Does the Block Universe of Physics Mean Time is an Illusion?

6 Comments
/
I have written many Insights (and coauthored an entire book) explaining how the puzzles, problems, and paradoxes of modern physics can be attributed to…
flight simulator

Introduction to Pitot-Static Systems in Gliders

1 Comment
/
Like many others, I have been seeking new and fun things to do during a pandemic.   I decided on the new Microsoft Flight Simulator 2020, but the Condor…
mechanical conservation of energy

Why Bother Teaching Mechanical Energy Conservation?

7 Comments
/
Note: It is assumed that the reader has read part I and part II of the series.Is Mechanical Energy Conservation Free of Ambiguity? Can We Do Better…
kerr spacetime centrifugal force

Centrifugal Force Reversal in Kerr Spacetime

0 Comments
/
In this article we will analyze "centrifugal force reversal" in Kerr spacetime, similar to what was done for Schwarzschild spacetime in a previous Insights…
strings waves

Physically Reasonable Waves on a String

4 Comments
/
Introduction Physics teachers who are either writing physics questions that deal with waves on a string, or setting up equipment for a class lab or demo…
Physics Olympiad Corrections

Corrections to the Australian Physics Olympiad Questions and Solutions

3 Comments
/
ref: asi.edu.au/programs/past-exams/physics-olympiad-past-exams/ Classification of issues: [1*] Quibble regarding solution. [2*] Clearer problem description…
physics mysteries

A Principle Explanation of the "Mysteries" of Modern Physics

79 Comments
/
All undergraduate physics majors are shown how the counterintuitive aspects ("mysteries") of time dilation and length contraction in special relativity…
Compton Scattering

Anatomy of Compton Scattering

0 Comments
/
Introduction In this article we take as our starting point the original equations which Compton drew up and solved in his ground-breaking 1925 article:  From…
Twins Paradox

The Twin Paradox for Freely-falling Observers

1 Comment
/
The "twin paradox" is often discussed in the introductory treatment of special relativity. Under "twin paradox" we understand the fact that if two twins…
android ringtone

Create an Android Ringtone Picker Using the Ringtonemanager Class

3 Comments
/
In this article, I will show you how to create a ringtone picker using the RingtoneManager class in Android. You will be able to get the list of tones,…
artificial intelligence

The Rise of AI in Classrooms, Labs and Industry – Part 3

0 Comments
/
We asked our PF Advisors “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?”. We got so many…
artificial intelligence

The Rise of AI in STEM - Part 2

0 Comments
/
We asked our PF Advisors “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?”. We got so many…
artificial intelligence

The Rise of Artificial intelligence in STEM Labs, Classrooms, and Industry

1 Comment
/
We asked our PF Advisors "How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?". We got so many great…
jrmichler engineer interview

Interview with Engineer jrmichler

0 Comments
/
Today we get to know a little more about Engineering Mentor jrmichler! Tell us a bit about your education and academic years Two years college (UW-Madison)…
electromagentic waves traverse

Are Electromagnetic Waves Always Transverse?

5 Comments
/
In this insight we shall endeavor in the realm of classical electrodynamics and examine whether EM waves are always transverse. We shall make use of Jefimenko's…
calculus

How to Solve Second-Order Partial Derivatives

1 Comment
/
Introduction A frequent concern among students is how to carry out higher order partial derivatives where a change of variables and the chain rule are…
pressure is a source of gravity

Is Pressure A Source Of Gravity?

11 Comments
/
In a previous series of articles, I posed the question "Does Gravity Gravitate?" and explained how, depending on how you interpreted the terms "gravity"…
Compton Scattering

Massive Meets Massless: Compton Scattering Revisited

0 Comments
/
Introduction In a previous article entitled "Alternate Approach to 2D Collisions" we analysed collisions between a moving and stationary object by defining…
Science Authority

Is Science An Authority?

66 Comments
/
In a previous article, I discussed why scientists (among others) are almost never interested in considering a new theory proposed by a non-scientist: because…
lerch and zeta functions

The Analytic Continuation of the Lerch and the Zeta Functions

0 Comments
/
Introduction In this brief Insight article the analytic continuations of the Lerch Transcendent and Riemann Zeta Functions are achieved via the Euler's…
dark energy supernova

Dark Energy Part 3: Fitting the SCP Union 2.1 Supernova Data

0 Comments
/
In Part 1 of this 3-part series, I explained kinematics in Einstien-deSitter (EdS) cosmology and in Part 2, I explained kinematics in ##\Lambda##CDM cosmology…
dark energy cosmology lcdm

Dark Energy Part 2: LCDM Cosmology

0 Comments
/
This is Part 2 of a 3-part series explaining evidence for so-called “dark energy” leading to a current positive cosmological acceleration. The evidence…
beginner guide to baryons

A Beginner's Guide to Baryons

9 Comments
/
Introduction At the beginning of the 20th century it was thought that all matter consisted of only three particles: the electron, the neutron and the…
symmetric spacetime

Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime

0 Comments
/
In the first two articles in this series, we looked at the Einstein Field Equation and Maxwell's Equations in a static, spherically symmetric spacetime.…
supernova refsdal

The Reappearance of Supernova (SN) Refsdal

0 Comments
/
Space is always changing. Over thousands of years, astronomers have attempted to understand the workings. Trying to explain astronomical events offers…
Dark Energy Cosmology Part 1

Dark Energy Part 1: Einstein-deSitter Cosmology

6 Comments
/
In this 3-part series, I want to motivate the (re)introduction of the cosmological constant ##\Lambda## into Einstein's equations of general relativity…
Evidence for Big Bang

Universe FAQ ‘Is there Evidence for the Big Bang?’

0 Comments
/
Evidence for the big bang can be provided from observational astronomy using Hubble’s law (redshift of galaxies) also known as the ‘Doppler effect’…
Cosmic Web Connections

The Evolution of the Universe, Cosmic Web and Connections

1 Comment
/
The universe was not perfectly uniform when it started, some areas had higher density than others. During the evolution of the universe, these areas of…
Gaia search for black holes

Gaia and the Race to Detect More Gravitational Waves

1 Comment
/
Gravitational waves (GW’s) are disturbances in spacetime produced by any massive object moving asymmetrically. However, only the most massive and most…

3 Possible Models For Why Uranus Spins on Its Side

4 Comments
/
Uranus spins on its side. Uranus has an obliquity (tilt) of 98º, making its axis of rotation closer to the ecliptic plane than any other planet. It is…

Black Holes Are Not Empty Voids. A Black Hole at the Heart!

9 Comments
/
Black Holes (BH’s) are curious because of their mysterious nature and unknown properties. BH’s are not empty voids. They are astronomical objects…
Integral Representations of Some Special Functions

A Path to Fractional Integral Representations of Some Special Functions

4 Comments
/
0. Introduction As for the reference material I have used the text Special Functions by Askey, Andrews, and Roy which covers much of the theorems here…
energy conservation can we do better

Can We Do Better Than Mechanical Energy Conservation?

6 Comments
/
Note: It is assumed that the reader has read part I of the series. Introduction The ambiguity and flaws discussed in part I can be resolved using the…
elastic ball collision

An Alternate Approach to Solving 2 Dimensional Elastic Collisions

4 Comments
/
Introduction This article follows on from the previous on an alternate approach to solving collision problems. In that article we determined the equal…
energy conservation ambiguity

Is Mechanical Energy Conservation Free of Ambiguity?

Introduction "Close to any question that is in the textbook, there is another question that has never been answered that is interesting." [Stephen Wolfram,…

How to Recognize Split Electric Fields

0 Comments
/
Introduction In a previous Insight, A New Interpretation of Dr. Walter Lewin’s Paradox, I introduced the fact that there are two kinds of E fields. …
Mass Generation

An Introduction to the Generation of Mass from Energy

17 Comments
/
Introduction This article is essentially an addition to the previous one on (mainly) inelastic collisions to include the particular case of inelastic…
What is Evolution

What is Evolution: A Beginner's Guide

0 Comments
/
Introduction to Evolution The study of evolution has dominated the field of biology for over a century. Explaining why the life we see is as it is fascinates…
Collision problems

An Alternative Approach to Solving Collision Problems

4 Comments
/
Introduction Collisions are very much a stock item in any school physics curriculum and students are generally taught about the use of the principles…
mary Somerville

Mathematician Mary Somerville Features in Google Doodle

0 Comments
/
The Google Doodle for 2 February 2020 celebrated Mary Somerville, the Scottish polymath and science writer, and with Caroline Herschel, the joint first…
perpetual motion machines

Why We Don't Discuss Perpetual Motion Machines (PMM)

12 Comments
/
Authorship Contributions From: AnorlundaYou may want to believe the article you read, or the video you saw, or you may be very proud of your PMM invention.…
c++ guide for beginners

Guide to C++ Programming For Beginners

0 Comments
/
Contents 1. Getting a C++ Compiler and Compiling Your First Program 2. Simple Datatypes and Declarations 3. Operators and Expressions 4. Input and…
fluid dynamics experiment

Accurate Fluid Dynamics By Video Analysis

3 Comments
/
IntroductionProviding accurate fluid dynamics experiments for undergraduate laboratories is challenging in several ways, including reproducibility,…
how to identify wood

Want to Tell One Wood from Another? Learn Basic Wood Anatomy

12 Comments
/
As a long-time woodworker I have an interest in being able to tell one wood from another and in the process of learning how to do that, I've developed…
Odd Sums

Explore the Fascinating Sums of Odd Powers of 1/n

3 Comments
/
The goal is to get a little bit closer to the values of the zeta function (ζ(s)) and the eta function (η(s)) for some odd values of s. This insight is…
Diffraction Grating Spectrometer.

Fundamentals of the Diffraction Grating Spectrometer

11 Comments
/
Introduction In this article we will discuss the fundamentals of the diffraction grating spectrometer.  The operation of the instrument is based upon…
hydrogen

Ionization Energy of Atomic Hydrogen

2 Comments
/
Introduction In previous articles relating to various transition energies in Hydrogen, Helium and Deuterium we have employed the following formula for…
grab bag science quiz

Grab Bag Science Quiz

16 Comments
/
Time to test your science knowledge with a fun 10 question quiz with random questions across all sciences. Difficulty is easy to medium. As always, post…
SOHCAHTOA

SOHCAHTOA: Seemingly Simple, Conceivably Complex

7 Comments
/
Preface My first experience with derivatives was seeing how they are obtained from the usual definition $$f'(x)=\underset{\text{$\Delta $x}\to 0}{\text{Lim}}\frac{f…
android rooting

An Intro to the Systemless Interface of Rooting Android Phones

8 Comments
/
What you can learn from this article:What is meant by rooting an Android phone Steps to take before proceeding to root your phone Google’s…