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For now, this intro has been adapted from Wikipedia.
More references, updates, and original work will be added over the next year.
The science wars is a series of intellectual exchanges, between scientific realists and postmodernist critics, about the nature of scientific theory and intellectual inquiry. They took place principally in the United States in the 1990s in the academic and mainstream press. Scientific realists (such as Norman Levitt, Paul R. Gross, Jean Bricmont and Alan Sokal) argued that scientific knowledge is real, and accused the postmodernists of having effectively rejected scientific objectivity, the scientific method, Empiricism, and scientific knowledge.
Postmodernists interpreted Thomas Kuhn‘s ideas about scientific paradigms to mean that scientific theories are social constructs, and philosophers like Paul Feyerabend argued that other, non-realist forms of knowledge production were better suited to serve people’s personal and spiritual needs.
Though much of the theory associated with ‘postmodernism’ (see poststructuralism) did not make any interventions into the natural sciences, the scientific realists took aim at its general influence. The scientific realists argued that large swaths of scholarship, amounting to a rejection of objectivity and realism, had been influenced by major 20th Century poststructuralist philosophers (such as Jacques Derrida, Gilles Deleuze, Jean-François Lyotard and others), whose work they declare to be incomprehensible or meaningless. They implicate a broad range of fields in this trend, including cultural studies, cultural anthropology, feminist studies, comparative literature, media studies, and science and technology studies. They accuse those postmodernist critics who did actually discuss science of having a limited understanding of it.
Higher Superstition: The Academic Left and Its Quarrels with Science, Paul R. Gross and Norman Levitt, 1994
Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science, Alan Sokal and Jean Bricmont, 1999
In 1996, Alan Sokal published an essay in the hip intellectual magazine Social Text parodying the scientific but impenetrable lingo of contemporary theorists. Here, Sokal teams up with Jean Bricmont to expose the abuse of scientific concepts in the writings of today’s most fashionable postmodern thinkers. From Jacques Lacan and Julia Kristeva to Luce Irigaray and Jean Baudrillard, the authors document the errors made by some postmodernists using science to bolster their arguments and theories. Witty and closely reasoned, Fashionable Nonsense dispels the notion that scientific theories are mere “narratives” or social constructions, and explored the abilities and the limits of science to describe the conditions of existence.
Social media and internet searches show a plethora of articles on “Planet X”, a vaguely worded term for some supposedly mysterious planet of apparently great importance.There are also conspiracy theories about the government or NASA supposedly hiding “Planet X” for some nefarious reason.
In science, we generally never use this phrase. When a scientist does say “Planet X” he/she merely means “any undetected planet in our solar system”.
Planets beyond Pluto
Scientists never quite said “Pluto isn’t a planet anymore.” That’s a misleading statement which muddies the waters. Here’s what really is going on.
Solar system is made of one star, several planets, comets, meteors, and gas & dust particles.
More recent, yet now outdated view
Solar system is made of one star, several planets, comets, meteors, and gas & dust particles.
The planets are either terrestrial (“Earth like”) or gas giants.
Solar system is made of one star, several planets, comets, meteors, and gas & dust particles.
The planets are now in categories:
terrestrial, gas giants, ice giants, or dwarf planets.
So all that really happened is that Pluto was moved from one general group, into a more specific group (dwarf planets.)
Here are some of the planets beyond Pluto, in our own solar system, already discovered. For size comparison they are shown as if they are near each other.
Ceres, Charon, Eris, Dysnomia, Pluto, Haumea, Makemake,
Why is it difficult to find new worlds?
Out there, space gets dark alarmingly fast. Planets twice as far away look 16 times dimmer: The intensity of the sunlight weakens by a factor of four going out and then four times again coming back.
At an orbital distance of 600 astronomical units (an AU is the distance between Earth and the sun), Planet Nine would be 160,000 times dimmer than Neptune is at 30 AU.
At 1,000 AU, it would appear more than 1 million times weaker.
“There’s really a brick wall, basically, at 1,000 AU,” said Kevin Luhman, an astronomer at Pennsylvania State University.” That’s partly why laying eyes on the planet has proven so tough.
Possible large planet orbiting beyond Pluto
Evidence that we’re seeing effects of a 10th planet
Swarm of asteroids instead of another plant
Science Bulletins: The Hunt for Planet X. American Museum for Natural History.
Astronomers find evidence of a ninth planet in the solar system – Caltech, Robert Hunt, Reuters
Next Generation Science Standards
Connections to Nature of Science: Science Models, Laws, Mechanisms, and Theories Explain Natural Phenomena.
A scientific theory is a substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment, and the science community validates each theory before it is accepted. If new evidence is discovered that the theory does not accommodate, then the theory is generally modified in light of this new evidence. (HS-ESS1-2),(HS-ESS1-6)
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
Some objects in the solar system can be seen with the naked eye. Planets in the night sky change positions and are not always visible from Earth as they orbit the sun. Stars appear in patterns called constellations, which can be used for navigation and appear to move together across the sky because of Earth’s rotation…. The solar system consists of the sun and a collection of objects, including planets, their moons, and asteroids that are held in orbit around the sun by its gravitational pull on them. This model of the solar system can explain tides, eclipses of the sun and the moon, and the motion of the planets in the sky relative to the stars.
The following has been excerpted from “Science matters because it works”, by The Logic of Science website, 4/23/17.
Why should you support science? Because it works! It’s crazy to me that I even have to say that, but this is where we are as a society. Various forms and degrees of science-denial are running rampant; attacks on science are being disseminated from the highest levels. Indeed, it has gotten to the point that scientists feel compelled to take to the streets to march for science and remind everyone of the fundamental fact that science works, and is unparalleled in its ability to inform us about reality and improve our world.
Just look around you. Everything that you see was brought to you by science.
- Batteries that power your electronic devices are a result of scientific advances in chemistry, as are the plastics that make up seemingly everything in our modern world.
- Planes that let you travel the world in mere hours were produced by our understanding of physics.
- Medicines that have doubled the human life expectancy came from biology, physiology, etc. Diseases that once claimed millions of lives each year are now almost unheard of thanks to advances in immunology, virology, etc.
- Even on topics where people frequently criticize science, like cancer, there have been great advances. Our ability to fight many cancers is improving, and, at the risk of appealing to anecdotes, I personally have family members who recovered from cancers that were untreatable just a few decades ago.
- Our entire modern world only exists because science works. Medicine, computers, cell phones, satellites, plastic, etc. all exist because science works.
Nevertheless, here we are, in a reality where some politicians [refer to global warming as a hoax], where countless celebrities go around promoting all manner of unscientific woo… a world where even a notion as ridiculous as believing that the earth is flat can enjoy a resurgence of popularity.
… At this point, inevitably lots of people are going to get offended and respond with something to the effect of, “I’m not anti-science, but…I disagree with the way that science is being done, I think that massive corporations are buying off scientists, I have anecdotes that don’t match the science, scientists have been wrong in the past, scientists are close-minded, etc.,”
Those aren’t valid responses [because] science is a method, and it either works, or it doesn’t. You can’t pick and choose when you want to accept it and when you want to reject it.
This brings me to two important points. First, the people who make, “I am not anti-science but…” arguments are nearly always people with no experience in science. They are people who are projecting their preconceptions onto a method that they know nothing about.
When people say that “scientists are just going along with the dogma of their fields” they are revealing how little they actually understand about how science operates… No one gets funding for blindly going along with something that everyone already knows. You only get funding for pushing boundaries and chasing novel ideas. Indeed, every great scientist was great precisely because they discredited the views of their day.
Arguments arise when science conflicts with someone’s personal beliefs.
For example, some people are happy enough to have science make more efficient batteries, predict tomorrow’s weather, cure their illnesses, etc., but the instant that it says that burning fossil fuels is bad, they turn on science and invent fanciful conspiracies, appeal to a minority of fringe researchers, cite discredited papers, etc.
Conversely, droves of people stand behind the science of climate change 100%, but when the same scientific method says that GMOs are safe, suddenly we are back in conspiracy land.
That’s not how this works… When thousands of papers conducted by countless scientists from all over the planet arrive at the same conclusion, you don’t get to reject that conclusion just because you don’t like it.
A final group of dissidents take things even further and directly question the validity of science itself. They claim that decades of research on vaccines is discredited by the simplistic notion that “mothers know best.” They ignore the scientific impossibility of homeopathy in favor of personal anecdotes. They insist that the fact that something has been used for thousands of years is more important than the fact that numerous studies have shown that it’s nothing but a placebo, and they embrace all manner of nonsense about energy fields, crystals, etc.
All of that is discredited by the obvious fact that science works: We had anecdotes and appeals to antiquity (or popularity, or maternal instincts) for thousands of years, but they got us nowhere. Science is the thing that allowed us to tell which of those anecdotes were based on causal relationships and which ones were based on spurious correlations,
Science is the thing that allowed us to know which natural remedies actually worked (e.g. aspirin) and which ones were hogwash. Further, science is the thing that let us improve on nature and synthesize purer and more concentrated forms of natural chemicals, as well as making medicines that aren’t even found in nature. For example, if you have diabetes and take insulin, you get that insulin not from nature, but rather from a GMO that was produced by science. Similarly, if you need surgery, you are going to want to be knocked out using the best anesthetic that science has to offer, rather than eating some herbs.
The history of tobacco actually illustrates this well. Tobacco was used medicinally for centuries by Native Americans, it was supported by countless anecdotes, it was 100% natural, mothers thought it was best for their children, etc. Today, however, we know that not only does it fail to cure illnesses, but it is extremely carcinogenic.
Why do we know that? Because of science! Careful and systematic studies revealed that all of those anecdotes, maternal instincts, etc. were wrong.
Now, someone may write a comment about the time that some scientists were paid off by Big Tobacco to support smoking, or the doctors who thought smoking was safe, but those are distortions: Sure, there was a transition period when evidence was still being accumulated and scientists and doctors were not convinced. Nothing in science changes overnight. But that period didn’t last because science prevailed.
Similarly, there were a minority of scientists that were paid off, and tobacco companies put tons of money and effort into creating the illusion that there was no scientific evidence that smoking was dangerous, but that was a smoke screen created by the tobacco companies, and their efforts ultimately failed.
This is the same thing that is happening today on many issues.
- The science on climate change, for example, is extremely clear. It is supported by thousands of studies and is agreed upon by virtually all climatologists. Nevertheless, fossil fuel companies have created an illusion of controversy. They have a handful of scientists that they publicize strongly, and they pour tons of money into promoting the notion that the science isn’t settled.
- The anti-vaccine movement is the same thing. The science for vaccines is solid, but they have a handful of “experts” and pump so much money into it that it appears that there is a conflict, even though this is a settled issue among medical experts.
- Similarly, big organic companies pump untold millions of dollars into opposing GMOs and making it appear that the science isn’t settled, even though nearly 2,000 studies have conclusively shown that GMOs are safe for humans and no worse (or even better) for the environment than traditional crops.
If you want life-saving medical breakthroughs to continue, then you need to support funding for agencies like the NIH. If you want to benefit from an enhanced understanding of the universe, then you need to support funding for things like the NSF. If you understand how many technological wonders have come from the space program and want more technological advances, then you need to support funding for NASA. I could go on, but hopefully you get my point. The way that I see it, our society is at something of a crossroads, and either we will fight for science, support it, and move forward because of it, or we will reject it, downplay it, and ignore it, in which case, at best, we will stagnate and halt our progress, and at worst, we will move backwards (e.g., increased disease outbreaks as vaccination rates fall). The choice between those two options seems pretty obvious to me.
This website is educational. Materials within it are being used in accord with the Fair Use doctrine, as defined by United States law.
§107. Limitations on Exclusive Rights: Fair Use. Notwithstanding the provisions of section 106, the fair use of a copyrighted work, including such use by reproduction in copies or phone records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use, the factors to be considered shall include: the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes; the nature of the copyrighted work; the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and the effect of the use upon the potential market for or value of the copyrighted work. (added pub. l 94-553, Title I, 101, Oct 19, 1976, 90 Stat 2546)
Andy Maldonado, on Quora, writes
An action potential is the way by which neurons communicate.
Neurons are negatively charged on the inside and positively charged on the outside.
This is due to the different concentrations of Na+, K+, Cl-, Ca2+, and charged proteins distributed both in and outside the neuron.
An action potential begins when a disruption of this distribution causes Na+ to flow into the neuron, through Na+ channels, causing the inside to become more positive.
The more positively charged inside of the neuron triggers adjacent voltage-gated Na+ channels to open and allow more ions to flow through.
The increase in charge inside the neuron triggers K+ channels to open – allowing for ions to flow outside of the cell, and thus lowering the inside charge back to its original state.
This increase and decrease in charge causes a wave-like motion of ions that propagates down the axon of a neuron – and ultimately causes the release of neurotransmitters from the dendrites – which stimulate the next neuron to either initiate or inhibit an action potential.
Action potentials trigger neuronal pathways which can stimulate or inhibit certain functions in our body. For example, action potentials in the motor region of the brain may stimulate a neural pathway with leads to the muscles in your arms resulting in flexion. Action potentials also facilitate communication between neuronal networks in the brain which allow us to have conscious thoughts, emotions, and memories.
As a nerve impulse travels down the axon, there is a change in polarity across the membrane.
The Na+ and K+ gated ion channels open and close in response to a signal from another neuron. At the beginning of action potential, the Na+ gates open and Na+ moves into the axon. This is depolarization. Repolarization occurs when the K+ gates open and K+ moves outside the axon. This creates a change in polarity between the outside of the cell and the inside. The impulse continuously travels down the axon in one direction only, through the axon terminal and to other neurons.
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-LS1-2. Develop and use a model to illustrate the key functions of animal body systems: Emphasis is on the primary function of the following body systems… nervous (neurons, brain, spinal cord).
College Board Science Standards
LSH-PE.5.5.4 Construct a simple representation of a feedback mechanism that maintains the internal conditions of a living system within certain limits as the external conditions change.
LSH-PE.5.5.5 Construct a representation of the interaction of the endocrine and nervous systems (e.g., hormones and electrochemical impulses) as they interact with other body systems to respond to a change in the environment (e.g., touching a hot stove). Explain how the representation is like and unlike the phenomenon it is representing.
This analysis is by Phil Plait, Mar 9, 2017
I will ask you to indulge me for a moment in a thought experiment. It’s not hard, and it leads to a startlingly simple yet powerful conclusion, one I think you may find both important and terribly useful.
Still, it starts with a big ask, so forgive me. And that is: Let’s make an assumption, one you’ve heard many times before. Let’s say that global warming is a hoax.
I know, I know. But go with this, here. So, yes, let’s say that climate change deniers —people like House Science, Space, and Technology Committee chairman Lamar Smith, Senator James Inhofe, and even Donald Trump himself— are right. Whatever the reasons (Chinese hoax, climatologist cabal clamoring colossal cash, carbon dioxide isn’t a powerful greenhouse gas, or just a liberal conspiracy), let’s say that the Earth is not warming up.
In that case, the temperatures we see today on average should be much like the ones we saw, say, 20 years ago. Or 50. Sure, you’d see fluctuations. In a given spot on a given day the temperature in 1968 might have been a degree warmer than it was in 1974, or three degrees cooler than in 2010. But what you’d expect is that over time, a graph showing the temperature would be pretty much flat, with lots of short-term spikes up and down.
Now, statistically speaking, you expect some records to be broken every now and again. Over time, every few years for a given day you’d get a record high, and every few years a record low. The details will change from place to place and time to time, but again, if the average temperature trend is flat, unchanging, then you would expect to see just as many record cold days as record warm days. There might be small deviations, like, say, a handful of more cool than warm days, but the difference would be very small depending on how many days you look at.
It’s like flipping a coin. On average, you should get a 50/50 split between heads and tails. But if you flip it 10 times, say, you wouldn’t be shocked to see seven heads and three tails. But if you flip it a thousand times, you’d really expect to see a very even split. Seeing 700 heads and 300 tails would be truly extraordinary.
So, if we remind ourselves of our basic assumption —global warming isn’t real— then we expect there to be as many record high days as there are record lows. Simple statistics.
So, what do we see?
Guy Walton, a meteorologist in Georgia, took a look at the data from the NOAA’s National Centers for Environmental Information. Whenever a weather station in the US breaks a record, high or low, it’s catalogued (Walton has more info on this at the link above). He found something astonishing: For February 2017, the number of record highs across the US recorded was 6,201.
The number of record lows? 128.
That’s a ratio of over 48:1. In just one month.
Again, if temperatures were flat over time, and record highs and lows were random fluctuations, you’d expect a ratio much closer to 1:1. In other words, out of 6329 records set in total, you’d expect there to be about 3165 record highs, and 3165 record lows.
For fans of statistics, with a total of 6329 records broken, one standard deviation is the square root of that, or about 80. So, sure, something like 3265 highs and 3064 lows wouldn’t be too unusual. If you start to see more of an imbalance than that, it would be weird.
Seeing 6201 record highs to 128 lows is very, very, very weird. Like, zero chance of that happening by accident.
Now, Phil, I can hear you thinking, that’s just for the US (2% of the planet) over one month. And you’ve told us before that weather isn’t climate; weather is what you expect now, climate is what you expect over long periods of time. So, maybe this is a fluke?
Walton notes that, if you look at records in the US going back to the 1920s, the six highest ratios of record highs to lows all occur since the 1990s. Huh.
And making this more global, a pair of Australian scientists looked at their country’s data, and found that their ratios were about even…until the 1960s. After that, highs always outnumber lows. From 2000-2014, record highs outnumbered lows there by 12:1.
The University Corporation for Atmospheric Research collated data from 1800 stations across the US and binned the data by decade — by decade, which is a huge sample; any deviation from a 1:1 ratio would be extraordinary over that timescale.
Source of the above image: RECORD HIGH TEMPERATURES FAR OUTPACE RECORD LOWS ACROSS U.S. The National Center for Atmospheric Research/UCAR, Nov 12, 2009
We are seeing far more record high temperatures than record lows in the US… and in other countries, too. Credit: UCAR
Huh. Not only are there more record highs than lows, the ratio between the two is getting higher with time.
So, looking back at our initial assumption — the Earth isn’t warming, and temperatures are flat— there’s a conclusion these data are screaming at us: That assumption is completely and utterly wrong.
And of course, all the evidence backs this up. All of it. Earth’s temperature is increasing. That’s because of the 40 billion tons of extra carbon dioxide humans put into the atmosphere every year (the amount we will see this year, expected to top 410 parts per million, has never been seen before in history as long as humans have walked the Earth). This CO2 allows sunlight to warm the Earth, but prevents all of it from escaping so that a little bit of extra heat remains behind, and that’s warming our planet.
Over time, we’re getting hotter. 2014 was a record hot year, beaten by 2015, itself beaten by 2016. In fact, 15 of the 16 hottest years ever recorded have been from 2001 – 2016. That’s exactly what you’d expect if we were getting warmer, and that means our initial assumption of hoaxery was dead wrong.
The science on this is so basic, the evidence of this so overwhelming, that “not a single national science academy disputes or denies the scientific consensus around human-caused climate change”, and also the overwhelming majority of scientists who study climate do, too.
Maybe you should listen to them, and not politicians who seem ideologically opposed to the science.
Or, you could flip a coin. But if it comes up science dozens of times more often than anti-science, well —and forgive me if I sound like a broken record— the conclusion is obvious.
Fair use: This website is educational. Materials within it are being used in accord with the Fair Use doctrine, as defined by United States law.
§107. Limitations on Exclusive Rights: Fair Use
Notwithstanding the provisions of section 106, the fair use of a copyrighted work, including such use by reproduction in copies or phone records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use, the factors to be considered shall include: the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes; the nature of the copyrighted work; the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and the effect of the use upon the potential market for or value of the copyrighted work. (added pub. l 94-553, Title I, 101, Oct 19, 1976, 90 Stat 2546)
From “You’re Not Going to Believe What I’m Going To Tell You”, from The Oatmeal/ Matthew Boyd Inman.
You’re Not Going to Believe What I’m Going To Tell You.
I’m going to tell you some things.
You’re not going to believe these things that I tell you.
And that’s Ok. You have good reason not to.
But I need you to keep listening, regardless of what you believe.
I don’t care if you’re liberal, conservative, or somewhere in between.
I don’t care if you’re a cat person, a dog person, or a tarantula person.
Morning person or night owl. iPhone or Android. Coke or Pepsi.
I don’t care. All I care about is that you read this to the end.
Sound good? Then let’s begin.
I’m caching a copy of www.maxwells-equations.com/ampere/amperes-law.php
This isn’t to negate the copyright of the original website, which I direct people to! I create backups like this on occasion, because even favorite teaching websites sometimes disappear (maybe the owner didn’t pay to renew the domain name.) And I wouldn’t want something so valuable to disappear.
On this page, we’ll explain the meaning of the last of Maxwell’s Equations, Ampere’s Law, which is given in Equation :
Ampere was a scientist experimenting with forces on wires carrying electric current. He was doing these experiments back in the 1820s, about the same time that Farday was working on Faraday’s Law. Ampere and Farday didn’t know that there work would be unified by Maxwell himself, about 4 decades later.
Forces on wires aren’t particularly interesting to me, as I’ve never had occassion to use the very complicated equations in the course of my work (which includes a Ph.D., some stints at a national lab, along with employment in the both defense and the consumer electronics industries). So, I’m going to start by presenting Ampere’s Law, which relates a electric current flowing and a magnetic field wrapping around it:
Equation  can be explained: Suppose you have a conductor (wire) carrying a current, I. Then this current produces a Magnetic Field which circles the wire.
The left side of Equation  means: If you take any imaginary path that encircles the wire, and you add up the Magnetic Field at each point along that path, then it will numerically equal the amount of current that is encircled by this path (which is why we write for encircled or enclosed current).
Let’s do an example for fun. Suppose we have a long wire carrying a constant electric current, I[Amps]. What is the magnetic field around the wire, for any distance r [meters] from the wire?
Let’s look at the diagram in Figure 1. We have a long wire carrying a current of I Amps. We want to know what the Magnetic Field is at a distance r from the wire. So we draw an imaginary path around the wire, which is the dotted blue line on the right in Figure 1:
Figure 1. Calculating the Magnetic Field Due to the Current Via Ampere’s Law.
Ampere’s Law [Equation 2] states that if we add up (integrate) the Magnetic Field along this blue path, then numerically this should be equal to the enclosed current I.
Now, due to symmetry, the magnetic field will be uniform (not varying) at a distance r from the wire. The path length of the blue path in Figure 1 is equal to the circumference of a circle of radius r: 2 x Pi x r.
If we are adding up a constant value for the magnetic field (we’ll call it H), then the left side of Equation  becomes simple:
Hence, we have figured out what the magnitude of the H field is. And since r was arbitrary, we know what the H-field is everywhere. Equation  states that the Magnetic Field decreases in magnitude as you move farther from the wire (due to the 1/r term).
So we’ve used Ampere’s Law (Equation ) to find the magnitude of the Magnetic Field around a wire. However, the H field is a Vector Field, which means at every location is has both a magnitude and a direction. The direction of the H-field is everywhere tangential to the imaginary loops, as shown in Figure 2. The right hand rule determines the sense of direction of the magnetic field:
Figure 2. The Magnitude and Direction of the Magnetic Field Around a Wire.
Manipulating the Math for Ampere’s Law
We are going to do the same trick with Stoke’s Theorem that we did when looking at Faraday’s Law. We can rewrite Ampere’s Law in Equation :
On the right side equality in Equation , we have used Stokes’ Theorem to change a line integral around a closed loop into the curl of the same field through the surface enclosed by the loop (S).
We can also rewrite the total current (I enclosed, I enc) as the surface integral of the Current Density (J):
So now we have the original Ampere’s Law (Equation ) rewritten in terms of surface integrals (Equations  and ). Hence, we can substitute them together and get a new form for Ampere’s Law:
Now, we have a new form of Ampere’s Law: the curl of the magnetic field is equal to the Electric Current Density. If you are an astute learner, you may notice that Equation  is not the final form, which is written in Equation . There is a problem with Equation , but it wasn’t until the 1860s that James Clerk Maxwell figured out the problem, and unified electromagnetics with Maxwell’s Equations.
Displacement Current Density
Ampere’s Law was written as in Equation  up until Maxwell. So let’s look at what is wrong with it. First, I have to throw out another vector identity – the divergence of the curl of any vector field is always zero:
So let’s take the divergence of Ampere’s Law as written in Equation :
So Equation  follows from Equations  and . But it says that the divergence of the current density J is always zero. Is this true?
If the divergence of J is always zero, this means that the electric current flowing into any region is always equal to the electric current flowing out of the region (no divergence). This seems somewhat reasonable, as electric current in circuits flows in a loop. But let’s look what happens if we put a capacitor in the circuit:
Figure 3. A Voltage Applied to A Capacitor.
Now, we know from electric circuit theory that if the voltage is not constant (for example, any periodic wave, such as the 60 Hz voltage that comes out of your power outlets) then current will flow through the capacitor. That is, we have I not equal to zero in Figure 3.
However, a capacitor is basically two parallel conductive plates separated by air. Hence, there is no conductive path for the current to flow through. This means that no electric current can flow through the air of the capacitor. This is a problem if we think about Equation . To show it more clearly, let’s take a volume that goes through the capacitor, and see if the divergence of J is zero:
Figure 4. The Divergence of J is not Zero.
In Figure 4, we have drawn an imaginary volume in red, and we want to check if the divergence of the current density is zero. The volume we’ve chosen, has one end (labeled side 1) where the current enters the volume via the black wire. The other end of our volume (labeled side 2) splits the capacitor in half.
We know that the current flows in the loop. So current enters through Side 1 of our red volume. However, there is no electric current that exits side 2. No current flows within the air of the capacitor. This means that current enters the volume, but nothing leaves it – so the divergence of J is not zero. We have just violated our Equation , which means the theory does not hold. And this was the state of things, until our friend Maxwell came along.
Maxwell knew that the Electric Field (and Electric Flux Density (D) was changing within the capacitor. And he knew that a time-varying magnetic field gave rise to a solenoidal Electric Field (i.e. this is Farday’s Law – the curl of E equals the time derivative of B). So, why is not that a time varying D field would give rise to a solenoidal H field (i.e. gives rise to the curl of H). The universe loves symmetry, so why not introduce this term? And so Maxwell did, and he called this term the displacement current density:
This term would “fix” the circuit problem we have in Figure 4, and would make Farday’s Law and Ampere’s Law more symmetric. This was Maxwell’s great contribution. And you might think it is a weak contribution. But the existance of this term unified the equations and led to understanding the propagation of electromagnetic waves, and the proof that all waves travel at the same speed (the speed of light)! And it was this unification of the equations that Maxwell presented, that led the collective set to be known as Maxwell’s Equations. So, if we add the displacement current to Ampere’s Law as written in Equation , then we have the final form of Ampere’s Law:
And that is how Ampere’s Law came into existance!
Intrepretation of Ampere’s Law
So what does Equation  mean? The following are consequences of this law:
- A flowing electric current (J) gives rise to a Magnetic Field that circles the current
- A time-changing Electric Flux Density (D) gives rise to a Magnetic Field that circles the D field
Ampere’s Law with the contribution of Maxwell nailed down the basis for Electromagnetics as we currently understand it. And so we know that a time varying D gives rise to an H field, but from Farday’s Law we know that a varying H field gives rise to an E field…. and so on and so forth and the electromagnetic waves propagate – and that’s cool.
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