Expert Math and Science Articles

Split Electric Fields

How to Recognize Split Electric Fields

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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.  One (Em) is generated whenever a source of emf is produced.  The other (Es) is the electrostatic field.  The Es field always terminates on free charges; the Em does not. …

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Mass Generation

An Introduction to the Generation of Mass from Energy

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Introduction This article is essentially an addition to the previous one on (mainly) inelastic collisions to include the particular case of inelastic…
Collision problems

An Alternative Approach to Solving Collision Problems

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Introduction Collisions are very much a stock item in any school physics curriculum and students are generally taught about the use of the principles…
perpetual motion machines

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

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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.…
fluid dynamics experiment

Accurate Fluid Dynamics By Video Analysis

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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

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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

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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

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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

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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

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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

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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

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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…
quantum entanglement

Answering Mermin's Challenge with Wilczek's Challenge

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Nearly four decades ago, Mermin revealed the conundrum of quantum entanglement for a general audience [1] using his "simple device," which I will refer…
Conservation of Spin Angular Momentum

Bell States and Conservation of Spin Angular Momentum

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In a recent thread, I outlined how to compute the correlation function for the Bell basis states\begin{equation}\begin{split}|\psi_-\rangle &=…
Kuhnian Revolution

Modern Physics Understood as an Unrecognized Kuhnian Revolution

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People often claim on Physics Forums and in the foundations community proper that quantum mechanics is "incomplete." Indeed, Lee Smolin recently wrote…
DC straight wire

Relativistic Treatment of the DC Conducting Straight Wire

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Introduction The direct-current-conducting infinitely long wire is often discussed in the context of relativistic electrodynamics. It is of course a completely…
Deuterium Lyman Alpha Line

Revisiting The Deuterium Lyman Alpha Line Experiment

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Introduction In this article we will be revisiting a somewhat understudied (and seemingly unrepeated) experiment to measure the Deuterium Lyman Alpha…
Solar Balmer Lines

Signature of the Sun: Analyzing the Solar Balmer Series Lines

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Introduction We are in many ways a fortunate generation having so many wonderful tools at our disposal on account of the "silicon revolution" . The advent…
bloatware android phones

Clearing Misconceptions and Some Tips on Debloating Android Phones

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What is bloatware? When you unbox your new phone, it comes with Android that is pre-installed by the manufacturer. This is termed as “stock firmware”.…
recursion in programming

Recursion in Programming and When to Use/Not to Use It

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Recursion is actually quite simple. It's a subroutine calling itself. Its surprising but some problems that look quite hard can be trivial using recursion…
Bohr’s Helium Lines

Understanding Bohr's Helium Lines

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Introduction In a previous article "Calculating the Balmer Alpha Line" we mentioned how accurate predictions of the spectral lines of singly ionized Helium…
maxwell magneto

Maxwell's Equations in Magnetostatics and Solving with the Curl Operator

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Introduction: Maxwell's equation in differential form ## \nabla \times \vec{B}=\mu_o \vec{J}_{total}+\mu_o \epsilon_o \dot{\vec{E}}  ##  with ## \dot{\vec{E}}=0…
what are the black hole thermodynamics

What Are the Thermodynamics of Black Holes? A 5 Minute Introduction

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Definition/Summary The four laws of black hole thermodynamics are as follows...The Zeroth Law Surface gravity [itex](\kappa)[/itex] is constant…
what is impedance

What is Impedance? A 5 Minute Introduction

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Definition/Summary The impedance of a load (a combination of components) in an AC current is a complex number [itex]Z\ =\ R+jX[/itex] where [itex]R[/itex]…
what if physics questions

How to Avoid Breaking Physics With Your "What If" Question

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We get a lot of "what if" questions here on Physics Forums. This article will explore three different types and then some suggestions for students who…
Learn Dimensional Analysis

Learn the Basics of Dimensional Analysis

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As a university teacher and as a PF member, I have often noted that students are largely unaware of or not using dimensional analysis to help them in their…
What is Mass Inflation

What is Mass Inflation? A 5 Minute Introduction

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Definition/Summary Abstract from Poisson and Israel's 1990 paper, 'Internal structure of black holes'-'The gravitational effects associated with the…
rotating room

How to Zip Through a Rotating Tunnel Without Bumping Into the Walls

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Preface While browsing through unanswered posts in the Classical Physics Workshop, I came across a gem at the link shown below.  For the reader's convenience,…
Balmer Alpha Line

Calculating the Balmer Alpha Line: Atomic Hydrogen

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Introduction Most readers acquainted with the hydrogen spectrum  will be familiar with the set of lines in the visible spectrum representing transitions…
spacetime maxwell

Maxwell's Equations in a Static, Spherically Symmetric Spacetime

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In the first article in this series, we looked at the Einstein Field Equations in a static, spherically symmetric spacetime. In this article, we are going…
What is potential energy

What is Potential Energy? A 5 Minute Introduction

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Definition/Summary Potential energy is simply another name for (minus) the work done by a conservative force.Since the work-energy theorem states…
How to Find Potential Functions

How to Find Potential Functions? A 10 Minute Introduction

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Definition/Summary Given a vector field ##\vec F(x,y,z)## that has a potential function, how do you find it? Equations $$\nabla \phi(x,y,z) = \vec F(x,y,z)$$…
Moment of Inertia

What is the Moment of Inertia? A 10 Minute Introduction

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Definition/Summary Moment of Inertia is a property of rigid bodies.It relates rotational force (torque) to rotational acceleration in the same way…
quantum superposition

Understanding Superposition

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IntroductionOne should first and foremost understand that superposition has both a mathematical an a physical meaning, or rather it originates as…
What is Entropy

On the Meaning of Entropy

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Introduction The intent of this article is to clarify the meaning of entropy and, while doing so, point out how a deeper analysis of entropy in classical…
What is a linear equation

What is a Linear Equation? A 5 Minute Introduction

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Definition/Summary A first order polynomial equation in one variable, its general form is [itex]Mx+B=0[/itex] where x is the variable. The quantities…
Einstein Field Equation

The Einstein Field Equation in a Static, Spherically Symmetric Spacetime

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This will be the first of several articles which will provide, for reference, useful equations for static, spherically symmeetric spacetimes. This is a…
What are significant figures

What are Significant Figures? A 5 Minute Introduction

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Definition/Summary Significant figures (commonly called "sig figs") are the number of figures (digits) included when rounding-off a number.For example,…
writing proofs

How Most Proofs Are Structured and How to Write Them

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... or the answer to: "I have no idea where to start!" Proofs in mathematics are what mathematics is all about. They are subject to entire books, created…
Camera Lens Physics

Lens Performance Testing: Evaluating a Camera Lens

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I've done plenty of imaging performance testing on a variety of systems, from millimeter wave through UV. Until very recently, such testing required expensive…
Quantum Mechanical Commutator

The Classical Limit of Quantum Mechanical Commutator

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The Classical Limit of Commutator (without fancy mathematics) Quantum mechanics occupies a very unusual place among physical theories: It contains classical…
Minkowski Spacetime

Precession in Special and General Relativity

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The Absolute Derivative In relativity we typically deal with two types of quantities: fields, which are defined everywhere, and particle properties, which…
What is a fibre bundle

What is a Fibre Bundle? A 5 Minute Introduction

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Definition/Summary Intuitively speaking, a fibre bundle is space E which 'locally looks like' a product space B×F, but globally may have a different…
What are real numbers

What is a Real Number? A 5 Minute Introduction

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Definition/Summary The real numbers are most commonly encountered number system, familiar to the layman via the number line, and as the number system…
Star Equations

Equations of State for Photon Gas and Relativistic Electron Gas

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This Insight develops equations of state that are useful in calculations about cosmology and about the insides of stars. The first calculation is for a…
What is the double split

What is the Double Slit? A 5 Minute Introduction

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Definition/Summary The double slit is a simple configuration used to demonstrate interference effects in waves.Equations At distances that are…
integration by parts

What is Integration By Parts? A 5 Minute Introduction

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Definition/Summary In this article, we shall learn a method for integrating the product of two functions. This method is derived from the 'product rule'…
rules of quantum mechanics

The 7 Basic Rules of Quantum Mechanics

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For reference purposes and to help focus discussions on Physics Forums in interpretation questions on the real issues, there is a need for fixing the common…
Quantum Particles

Clarifying Common Issues with Indistinguishable Particles

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Commonly there is a lot of imprecision in talking about ''indistinguishable'' (or ''identical'') particles, even in serious work. This Insight article…
isotropy definition

A Formal Definition of Large-Scale Isotropy

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This Insight is part of my attempt to develop a formal definition of 'large-scale isotropy', a concept that is fundamental to most cosmology, but that…
What is a parabola

What is a Parabola? A 5 Minute Introduction

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Definition/Summary A parabola has many definitions, a classical one being, "A Parabola is the locus of all points equidistant from a given point (called…
Renewable Energy Power Grid

Renewable Energy Meets Power Grid Operations

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The electric power industry faces much turmoil in the coming decades.  The business model of of the electric utility company (public or private) may not…

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