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Earth’s magnetic field

Earth’s Magnetic Field

The Earth has a magnetic field. When we use a compass, we make use of this field. So we’re tempted to view the Earth as a big rock with a giant bar magnet stuck through it.

But this isn’t at all how it really works: The Earth has a molten metal core, surrounded by a highly metallic shell of magma.  Electrons move through this metal  – and the motion of electrons – as will learn in this chapter – creates a magnetic field!

The Earth itself is slowly spinning, so we end up with slow-moving currents within the Earth. These currents affect the flow of electrons, thus affecting the resulting magnetic field.

Here is the “obvious” model of Earth’s magnetic field (it’s wrong)


The red pointer in a compass is attracted by Earth’s own magnetism (sometimes called the geomagnetic field—”geo” simply means Earth).

As English scientist William Gilbert explained about 400 years ago, Earth behaves like a giant bar magnet with one pole up in the Arctic (near the north pole) and another pole down in Antarctica (near the south pole).

Earth’s magnetic field is actually quite weak compared to the “macho” forces like gravity and friction that really dominate our lives.

For a compass to be able to show up the relatively tiny effects of Earth’s magnetism, we have to minimize the effects of these other forces.

That’s why compass needles are :

* lightweight (so gravity has less effect on them)

* mounted on frictionless bearings (so less resistance for the magnetic force to overcome)



“Where the Earth’s magnetic field comes from, Chris Rowan

The Earth’s magnetic field may approximate to a simple dipole, but explaining precisely how that dipole is generated and maintained is not simple at all. The field originates deep in the Earth, where temperatures are far too high for any material to maintain a permanent magnetisation.

The dynamism that is apparent from the wandering of the magnetic poles with respect to the spin axis (secular variation), and the quasi-periodic flips in field polarity, also suggest that some process is actively generating and maintaining the geomagnetic field. Geophysicists therefore look to the most dynamic region in the planetary depths, the molten outer core, as the source of the force that directs our compass needles…

The Earth’s interior generates a magnetic field. It reaches out into space.



This magnetic field protects us from some types of radiation

Earth’s North geographic pole has a South magnetic field

The “north” pole of a compass – by definition – is pulled to a “south” magnetic pole.

If we hold a compass in our hands, and call the part pointing to the land of Polar bears “north”, then we’d have to call the part attracting it “south.”

Earth North Geographic Pole South Magnetic Pole

How a planet becomes a magnet

Earth’s magnetic field single-handedly protects life on this planet from a deadly case of solar wind-burn, By Bernie Hobbs


Magnetic field reversals

The magnetic field of the Earth is not stable; it has flip-flopped throughout geologic time.

Evidence: (to be added)

“In the meantime, scientists are working to understand why the magnetic field is changing so dramatically. Geomagnetic pulses, like the one that happened in 2016, might be traced back to ‘hydromagnetic’ waves arising from deep in the core1. And the fast motion of the north magnetic pole could be linked to a high-speed jet of liquid iron beneath Canada2.”

Earth’s magnetic field is acting up and geologists don’t know why. Nature Jan 19

Geomagnetic acceleration and rapid hydromagnetic wave dynamics in advanced numerical simulations of the geodynamo, Aubert, Julien, Geophys. J. Int. 214, 531–547 (2018).

An accelerating high-latitude jet in Earth’s core. Livermore, P. W., Hollerbach, R. & Finlay, C. C. Nature Geosci. 10, 62–68 (2017).


App: The solar wind and Earth’s magnetic field


Learning about Earth’s magnetic field: ESA’s Swarm mission



Our school is right by Boston Harbor – learning about the sea is second nature to many of our staff. So we love to tie maritime history and science into our curriculum.

Binnacle maritime

Photo by RK

As you enter our school, you pass by a binnacle – what was it used for?

A binnacle is a waist-high case, found on the deck of a ship, that holds the compass.

It is mounted in gimbals to keep it level while the ship pitched and rolled.

It also has a mechanism to compensate for errors in detecting the Earth’s magnetic field.

Every ship’s captain would use one, for navigating in and out of Boston Harbor, and around the world.


Here we see Boston Harbor – now let’s get in to how the binnacle works!

Boston Harbor Islands map

This map is from mass.gov/eea/images/dcr


Why did we need to develop the binnacle?

Excerpted from Magnetic Deviation: Comprehension, Compensation and Computation by Ron Doerfler  

Today, radio navigational systems such as LORAN and GPS, and inertial navigation systems with ring and fiber-optic gyros, gyrocompasses and the like have reduced the use of a ship’s compass to worst-case scenarios. But this triumph of mathematics and physics over the mysteries of magnetic deviation, entered into at a time when magnetic forces were barely understood and set against the backdrop of hundreds of shipwrecks and thousands of lost lives, is an enriching chapter in the history of science.

The Sources of Compass Error

Ron Doerfler writes:

Compasses on ships fail to point to true (geographic) north due to two factors:

Magnetic variation (or magnetic declination) – the angle between magnetic north and geographic north due to the local direction of the Earth’s magnetic field, and

Magnetic deviation – the angle between the compass needle and magnetic north due to the presence of iron within the ship itself.

The algebraic sum of the magnetic variation and the magnetic deviation is known as the compass error. It is a very important thing to know.

Magnetic Variation

Magnetic variation has been known from voyages since the early 1400s at least. Certainly Columbus was distressed as he crossed the Atlantic to find that magnetic north and true north (from celestial sightings) drifted significantly…

We now know that the locations of the Earth’s magnetic poles are not coincident with the geographic poles—not even close, really—and they are always wandering around.

magnetic north pole deviation

Image from commons.wikimedia.org, Magnetic_North_Pole_Positions. Red circles mark magnetic north pole positions as determined by direct observation, blue circles mark positions modelled using the GUFM model (1590–1980) and the IGRF model (1980–2010) in 2 year increments.


What’s the difference between where a compass needle points (magnetic north) and the geographic north pole? This is called the declination  It’s smallest near the equator, but generally gets large as one moves towards the poles.

On this map, the green arrows – the direction from the compass – point towards the magnetic north. The red arrows point towards the geographical north pole.

Notice how the left location (in Pacific ocean) shows the compass point a bit east of where we’d hope it would point; in the right location (in Atlantic Ocean) it shows the compass point a bit west of where we’d hope it points.

There’s also a special line where the magnetic north and geographic north point in the same direction.

Magnetic Declination

Image from Drillingformulas.com by Rachain J i


Here we can see how many degrees of deviation there are – the # of degrees between where the compass points, and where the north pole is. But – wait for it – the image is changing? The magnetic fields are significantly changing every year!

Estimated declination contours by year

from USGS.gov, faqs, what is declination


Magnetic Deviation

Ron Doerfler writes

There is an additional effect on the compass needle that took much longer to appreciate and even longer to understand. This magnetic deviation is due to the iron in a ship…

The first notice in print of this effect was by Joao de Castro of Portugal in 1538, in which he identified “the proximity of artillery pieces, anchors and other iron” as the source.

As better compass designs appeared, a difference in compass readings with their placement on the same ship became more apparent. Captains John Smith and James Cook warned about iron nails in the compass box or iron in steerage, and on Cook’s second circumnavigation William Wales found that changes in the ship’s course changed their measurements of magnetic variation by as much as 7°.

Here we see a modern naval vessel, with it’s own magnetic field. As a metal ship moves through Earth’s magnetic field, an electric current is produced within all that metal – and that current produces it’s own magnetic field. This field can affect the ship’s compass. That’s why a binnacle is designed to be adjustable, to compensate for this field. – RK

Degaussing magnetic field ship

image from slideplayer.com/slide/1632522/


Ron Doerfler writes

Captain Matthew Flinders (1774-1815) spent years in the very early 1800s on voyages to investigate these effects…. [he] eventually discovered that an iron bar placed vertically near the compass helped overcome the magnetic deviation. This Flinder’s bar is still used today in ships’ binnacles.


Apps & Interactives

NOAA Historical Magnetic Declination


Hands-on Activity: Nautical Navigation. Teachengineering.org




Educational opportunities and museums




Important components

Quadrantal spheres (spherical quadrantal correctors)

Hood, over the compass bowl

flinders bar (vertical, soft iron corrector)

Learning Standards

Ocean Literacy Scope and Sequence for Grades K-12
6. The ocean and humans are inextricably interconnected: From the ocean we get foods, medicines, and mineral and energy resources. In addition, it provides jobs, supports our nation’s economy, serves as a highway for transportation of goods and people, and plays a role in national security.

Massachusetts 2016 Science and Technology/Engineering (STE) Standards
7.MS-PS2-5. Use scientific evidence to argue that fields exist between objects with mass, between magnetic objects, and between electrically charged objects that exert force on each other even though the objects are not in contact.

HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion is a mathematical model describing change in motion (the acceleration) of objects when acted on by a net force….{forces can include magnetic forces}

HS-PS3-5. Develop and use a model of magnetic or electric fields to illustrate the forces and changes in energy between two magnetically or electrically charged objects changing relative position in a magnetic or electric field, respectively.

History standards

National Standards for History Basic Edition, 1996
5-12 Identify major technological developments in shipbuilding, navigation, and naval warfare and trace the cultural origins of various innovations.

Massachusetts History and Social Science Curriculum Framework
The Political, Intellectual and Economic Growth of the Colonies. Explain the importance of maritime commerce in the development of the economy of colonial Massachusetts, using historical societies and museums as needed.

National Curriculum Standards for Social Studies: A Framework for Teaching, Learning, and Assessment, National Council for the Social Studies, 2010.


Ampère’s circuital law

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 [1]:


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 [2] 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 [2] 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 encircled current 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 [2] 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 [3] 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 [2]) 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 [2]:


On the right side equality in Equation [4], 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 [2]) rewritten in terms of surface integrals (Equations [4] and [5]). 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 [6] is not the final form, which is written in Equation [1]. There is a problem with Equation [6], 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 [6] 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 [6]:

divergence of ampere's law [Equation 8]

So Equation [8] follows from Equations [6] and [7]. 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:

a-c circuit with a capacitorFigure 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 [8]. To show it more clearly, let’s take a volume that goes through the capacitor, and see if the divergence of J is zero:

divergence not zero when a capacitor is presentFigure 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 [8], 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:

displacement current density [Equation 9]

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 [6], then we have the final form of Ampere’s Law:

final form of Ampere's Law [Equation 10]

And that is how Ampere’s Law came into existance!

Intrepretation of Ampere’s Law

So what does Equation [10] 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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Magnetism MCAS topics

See the lesson here Kaiserscience -> Physics -> Electromagnetism -> “Magnetism-and-electricity”

MCAS Open Response: sample questions with full solutions

MCAS questions

Which of the following forces allow a battery-powered motor to generate mechanical energy? (2014)
A. magnetic and static             B. electric and magnetic
C. static and gravitational    D. electric and gravitational


Which of the following statements describes an electric generator? (2013)
A. A magnet is rotated through a coil of wire to produce an electric current.
B. Electric potential in a rotating coil of wire creates a permanent magnet.
C. An electrical current causes a coil of wire to rotate in a magnetic field.
D. Forces from a permanent magnet allow a coil of wire to rotate.


2012 magnet wire question MCAS


This next one is from 2010

2010 MCAS galvanometer magnetic


Which of the following would cause the galvanometer needle to move?

A. wrapping additional wire around the tube
B. uncoiling the wire wrapped around the tube
C. moving a magnet back and forth inside the tube
D. moving an aluminum block up and down inside the tube


This next one is from 2009

Precise measuring instruments require shock absorbers to eliminate small vibrations that can affect the results of an experiment. One type of shock absorber that can be used is an electromagnet that repels a magnetic platform placed above it. Which of the following setups would provide the greatest lift to the platform?

2009 MCAS magnetic platform

Origin of magnetism

Also see https://kaiserscience.wordpress.com/physics/electromagnetism/sources-of-magnetism/

and https://kaiserscience.wordpress.com/physics/electromagnetism/magnetism/

Where does magnetism come from?

I’ve heard that special relativity makes the concept of magnetic fields irrelevant, replacing them with relativistic effects between charges moving in different velocity frames. Is this true? If so, how does this work?

Luboš Motl, a Czech theoretical physicist, replies:

Special relativity makes the existence of magnetic fields an inevitable consequence of the existence of electric fields. In the inertial system B moving relatively to the inertial system A, purely electric fields from A will look like a combination of electric and magnetic fields in B. According to relativity, both frames are equally fit to describe the phenomena and obey the same laws.

So special relativity removes the independence of the concepts (independence of assumptions about the existence) of electricity and magnetism. If one of the two fields exists, the other field exists, too. They may be unified into an antisymmetric tensor, FμνFμν.

However, what special relativity doesn’t do is question the independence of values of the electric fields and magnetic fields. At each point of spacetime, there are 3 independent components of the electric field E⃗ E→ and three independent components of the magnetic field B⃗ B→: six independent components in total. That’s true for relativistic electrodynamics much like the “pre-relativistic electrodynamics” because it is really the same theory!

Magnets are different objects than electrically charged objects. It was true before relativity and it’s true with relativity, too.

It may be useful to notice that the situation of the electric and magnetic fields (and phenomena) is pretty much symmetrical. Special relativity doesn’t really urge us to consider magnetic fields to be “less fundamental”. Quite on the contrary, its Lorentz symmetry means that the electric and magnetic fields (and phenomena) are equally fundamental. That doesn’t mean that we can’t consider various formalisms and approximations that view magnetic fields – or all electromagnetic fields – as derived concepts, e.g. mere consequences of the motion of charged objects in spacetime. But such formalisms are not forced upon us by relativity.


Terry Bollinger , an American computer scientist who works at the MITRE Corporation, replies:

Although the relationship between special relativity and magnetic fields is often stated as making magnetic fields irrelevant, this is not quite the correct way to say it.

What actually disappears is the need for magnetic attractions and repulsions. That’s because with the proper choice of motion frames a magnetic force can always be explained as a type of electrostatic attraction or repulsion made possible by relativistic effects.

The part that too often is overlooked or misunderstood is that these changes in the interpretation of forces does not eliminate the magnetic fields themselves. One simple way to explain why this must be true is that if it was not, a compass would give different readings depending on which frame you observed it from. So to maintain self-consistency across frames, magnetic fields must remain in place, even when they no longer play a role in the main attractive or repulsive forces between bodies.

One of the best available descriptions of how special relativity transforms the role of magnetic fields can be found in the Feynman Lectures on Physics. In Volume II, Chapter 13, Section 13-6, The relativity of magnetic and electric fields, Feynman describes a nicely simplified example of a wire that has internal electrons moving at velocity v through the wire, and an external electron that also moves at v nearby and parallel to the wire.

Feynman points out that in classical electrodynamics, the electrons moving within the wire and the external electron both generate magnetic fields that cause them to attract. Thus from the view of human observers watching the wire, the forces that attract the external electron towards the wire are entirely magnetic.

However, since the external and internal electrons move in the same direction at the same velocity v, special relativity says that an observer could “ride along” and see both the external and internal electrons as being at rest.

Since charges must be in motion to generate magnetic fields, there can in this case be no magnetic fields associated with the external electron or the internal electrons.

But to keep reality self-consistent, the electron must nonetheless still be attracted towards the wire and move towards it! How is this possible?

This is where special relativity plays a neat parlor trick on us.

The first part of the trick is to realize that there is one other player in all of this:

The wire, which is now moving backwards at a velocity of -v relative to the motionless frame of the electrons.

The second part of the trick is to realize that the wire is positively charged, since it is missing all of those electrons that now look like they are sitting still.

That means that the moving wire creates an electric current composed of positive charges moving in the -v direction.

The third and niftiest part of the trick is where special relativity kicks in.

Recall than in special relativity, when objects move uniformly they undergo a contraction in length along the direction of motion called the Lorentz contraction.

I should emphasize that Lorentz contraction is not some kind of abstract or imaginary effect. It is just as real as the compression you get by squeezing something in a vice grip, even if it is gentler on the object itself.

Now think about that for a moment:

If the object is also charged at some average number of positive charges per centimeter, what happens if you squash the charged object so that it occupies less space along its long length?

Well, just what you think: The positive charges along its length will also be compressed, resulting in a higher density of positive charges per centimeter of wire.

The electrons are not moving from their own perspective, however, so their density within the wire will not be compressed. When it comes to cancelling out charge, this is a problem! The electrons within the wire can no longer fully cancel out the higher density of positive charges of the relativistically compressed wire, leaving the wire with a net positive charge.

The final step in the parlor trick is that since the external electron has a negative charge, it is now attracted electrostatically to the wire and its net positive charge.

So even though the magnetic fields generated by the electrons have disappeared, a new attraction has appeared to take its place!

Now you can go through all of the details of the math and figure out the magnitude of this new electrostatic attraction.

However, this is one of those cases where you can take a conceptual shortcut by realizing that since reality must remain self-consistent – no matter what frame you view if from – the magnitude of this new electrostatic attraction must equal the magnetic attraction as seen earlier from the frame of a motionless wire.

(If you do get different answers, you need to look over your work!)

But what about the other point I made earlier, the one about the magnetic field not disappearing? Didn’t the original magnetic field disappear as soon as one takes the frame view of the electrons?

Well, sure. But don’t forget: Even though the electrons are no longer moving, the positively charged wire is moving and will generate its own magnetic field. Furthermore, since the wire contains the same number of positive charges as electrons in the current, all moving in the opposite (-v) direction, the resulting magnetic field will look very much like the field originally generated by the electrons.

So, just as the method of attraction switches from pure magnetic to pure electrostatic as one moves from the wire frame to the moving electron frame, the cause of the magnetic field also switches from pure electron generated to pure positive-wire generated. Between these two extremes are other frames in which both attraction and the source of the magnetic field become linear mixes of the two extreme cases.

Feynman briefly mentions the magnetic field generated by the moving positive wire, but focuses his discussion mostly on the disappearance of the electron-generated magnetic fields. That’s a bit unfortunate, since it can leave a casual reader with the incorrect impression that the magnetic fieldas a whole disappears.

It does not, since that would violate self-consistency by making a compass (e.g., the magnetic dipole of that external electron) behave differently depending on the frame from which you observe it.

The preservation of the magnetic field as the set of particles generating it changes from frame to frame is in many ways just as remarkable as the change in the nature of the attractive or repulsive forces between objects, and is worth noting more conspicuously.

Finally, all of these examples show that the electromagnetic field really is a single field, one whose overt manifestations can change dramatically depending on the frame from which they are viewed. The effects of such fields, however, are not up for grabs. Those must remain invariant even as the apparent mechanisms change and morph from one form (or one set of particles) to another.

Does special relativity make magnetic fields irrelevant? Physics StackExchange


Also see

The Feynman Lectures. 13–6 Magnetostatics. The relativity of magnetic and electric fields


Special Relativity in 14 Easy (Hyper)steps

14. Why there are magnetic fields


What are fields?

What are gravitational fields? Electric fields? Magnetic fields? the electromagnetic field?

What do physicists mean by the term “field”?

Let’s start by seeing how we describe stuff – anything – that exists in space.

Imagine our universe is flat. We could describe what’s going on at any point by defining a 2D grid, like graph paper.

We could use a 2D field to show the temperature at any location.

2-d field representing wind speed


Our universe is 3D.

We need 3 dimensions – 3 axes – to describe any point in space.

This image shows an empty universe, with nothing in it.

Now imagine this 3D grid extending through our world:

(indoor 3D climbing array by Croatian-Austrian artists Sven Jonke, Christoph Katzler and Nikola Radeljković.)

Now let’s imagine a 3D field extending through all of space – but this isn’t just a mathematical tool.

But rather, we discovered that all of space is filled with several different fields.

These fields exist everywhere – on Earth and in space, between you and me. They are within our bodies, and they extend to the visible boundaries of the universe

These fields are not a hypothesis or idea; they are absolutely real.

There are two basic things that the universe is made of:

particles (like protons, electrons, neutrons)


Here we see someone throw up a handful of magnetic iron filings around a suspended magnet. Magnify this image and look carefully.

We see the tiny pieces of metal pulled along the magnetic field lines.

GIF Visualizing a magnetic field iron filings

Consider a horseshoe magnet – it’s a 3D object, with a 3D magnetic field invisibly emanating from it. How can we visualize this invisible field? How about tossing in a few thousand small iron filings! 🙂

At every single point in our universe there is an electric field, a magnetic field, a gravitational field, and more!

As a magnet moves close to you, the values at each point in this magnetic field change. We can’t see it with our eyes or feel it with our fingers – but we can measure it by seeing the effect it has on a compass. We can see the effect it has on the magnetometer built into your cell phone (and yes, there’s an app for that!)

Physics Toolbox Magnetometer: google play


Using art and science to visualize Wi-Fi fields

Wi-Fi is a special type of radio signal.

Radio is part of the electromagnetic spectrum.

So as Wi-Fi signals propagate, they change the value of the EM field throughout space.

Human eyes can’t see this directly, but

“Nickolay Lamm has already made the invisible visible with a project that showed what Wi-Fi would look like if we could see it, but for his latest series of images, the artist has turned his attention to cell phones. Cell phone networks across the country are made up of multiple hexagonal areas, each of which is called a cell, that you can clearly make out in the images. The hexagonal grid is efficient, as each cell tower sits at the intersection of three cells, and each of the three directional antennas on top of the tower covers a 120-degree slice of the landscape.”

“To make sure his illustrations were as accurate as possible, Lamm worked with two professors of electrical and computer engineering: Danilo Erricolo at the University of Illinois at Chicago and Fran Harackiewicz at Southern Illinois University in Carbondale.”

What if you had an app on a tablet that let you (roughly) visualize a part of the EM field in this very room?

To be clear, no single device can measure every part of the EM field. One would need different sensors to record each part of it. Even when many parts are recorded, there is no useful way to show all of it at once: you’d be piling multiple images on top of each other, leading to a dense, impossible-to-see mess. But you can use a device to measure any one of these, and then display this data on its own:

The EM field can include:

  • radio waves / WiFi signals

  • microwaves

  • infrared

  • visible light

  • ultraviolet

An app created by Richard Vijgen, called Architecture of Radio, visualizes the overlapping signals that envelop us — from cell towers, WiFi routers, and even satellites flying overhead.  The app, at the moment, is site-specific to an installation in Germany. It uses GPS to get the user’s location then finds nearby cell towers using OpenCellID, and has been custom-programmed to map the WiFi routers and Ethernet cables in the exhibition space. It also uses OpenCellID to predict any satellites that might pass overhead. The app then uses this data to visualize the signals swirling around the exhibition-goers, showing what the project’s website refers to as the “infosphere” that we all live in now.

This app lets you visualize the WiFi signals pulsing around you

Android app. Architecture of Radio, Studio Richard Vijgen

Website: Architecture of radio

Now understand that our entire universe is filled with such fields:

AP Physics Learning Objectives

Essential Knowledge 2.A.1: A vector field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a vector.

a. Vector fields are represented by field vectors indicating direction and magnitude.
b. When more than one source object with mass or electric charge is present, the field value can be determined by vector addition.
c. Conversely, a known vector field can be used to make inferences about the number, relative size, and location of sources.

Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.

Essential Knowledge 2.A.2: A scalar field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a scalar. In Physics 2, this should include electric potential.
a. Scalar fields are represented by field values.
b. When more than one source object with mass or charge is present, the scalar field value can be determined by scalar addition.
c. Conversely, a known scalar field can be used to make inferences about the number, relative size, and location of sources.

Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.

Cool car built from a battery and two magnets 

Cool car built from a battery and two magnets How to make the simplest electric car toy from 1 battery and 2 magnets:
Put round magnets on either end of a AA battery and set it down on a sheet of tinfoil and watch it spin! It’s a homopolar motor, a simple electric motor that relies on the Lorentz effect to set it in motion.
If you take two circular magnets and slap them on the ends of a AA battery, the resulting axel will drive on a road of aluminum foil. This is called a homopolar motor and it’s one of the simplest machines you can build.

…the homopolar motor works because the combination of the flow of the electric current (from the battery) and the flow of the magnetic current produces a torque via the Lorenz force.

This short video explanation should give you a good idea of the principles involved.