Category: Natural World

Electromagnets

Electric Currents Generate Magnetic Fields (36.5)

An electric current in a wire creates a magnetic field around the wire. Image adapted from Wikimedia Commons User:Stannard.

Moving charges create magnetic fields. Currents moving through a wire are moving electric charges (electrons). Therefore, current-carrying wires generate a magnetic field around them.

Bending wires into a loop will create will create a magnetic field through the loop.

  • The more loops you have the stronger the magnetic field.
  • The magnets created by pushing a current through loops of wire is called an electromagnet.
  • If you use superconducting wire, you can create an extremely powerful superconducting magnet that can be used in magnetic levitation (maglev) trains.
Magnetic field through a coil of wire (with a current running through it). The more loops of the wire, the stronger the electric field.

Magnets Deflect the Movement of Charged Particles (36.6)

Moving charged particles create magnetic fields. So if a moving charged particle encounters a magnetic field the two magnetic fields will interact and the motion of the particle will be deflected.

A charged particle is deflected from it's forward motion when a magnetic field is turned on.

Note that the deflection only occurs when the particle is not traveling parallel to the magnetic field lines.

  • The big, old styled TV’s use this to shoot electrons at the screen to make the picture.
  • The Earth’s magnetic field deflects the charged particles ejected by the Sun, protecting the planet.
The Earth's magnetic field protects us from the solar wind. Image from NASA.

Interaction Between Magnets and Currents in Wires

Just like charged particles are deflected when they run into a magnetic field, charges running through a wire will create a magnetic field that will interact with external magnets to cause the wire to move.

  • The force on the wire is perpendicular both to the direction of the current and the lines of the magnetic field.
  • If you reverse the current in the wire (send it the other way) the force will be in the opposite direction.
The force resulting from a current is at right angles to the magnetic field and the current; the "right hand rule" is an easy way to remember this. Image adapted from User:Acdx on Wikimedia Commons.

You can use this principle to create a galvanometer, which is a device that detects electric currents, or to build motors.

A simple electric motor.

Earth’s Magnetic Field

Convection currents in the Earth’s molten, metalic outer core create the Earth’s magnetic field.

Because the pattern of convection changes over time, the Earth’s magnetic field:

  • Is not located at the north pole (axis of rotation).
  • Wanders: it moves a little each year.
  • Flips so its poles reverse every 800,000 years or so.
The location of the magnetic north pole changes with time. Image via the National Forest Service.

As lava cools, the magnetic minerals in it orient themselves with the Earth’s magnetic field. One way of telling how old basalt rocks on the seafloor are is by looking at the direction of their magnetic field. Since the Africa and the Americas are moving apart, slowly over millions of years, there is a suture in the Earth’s crust in the middle of the Atlantic ocean where new seafloor is made from erupting, under-sea volcanos. As a result, there are magnetic stripes all along the Atlantic Ocean (and all the other oceans too) that have recorded each time the Earth’s magnetic polarity has reversed.

Magnetic striping in oceanic crust. Image from the USGS.

The USGS has high-resolution geomagnetic maps.

Map of the remnent magnetism in the crust (focus on North America and North Atlantic). Via the USGS.

Gravity, the Electromagnetic Forces, and the Inverse Square Law

Calculating the forces between two charged particles (electric force), two magnets (the magnetic force), and two masses (the gravitational force) require remarkably similar equations. But, while electricity and magnetism are directly related (that’s why it’s called electromagnetism), gravity is its own fundamental force. Yet they all depend (inversely) on the square of the distance between the two objects creating the force, so they’re all said to obey some form of the inverse square law.

Gravitational Force (Fg)

The force exerted by two masses on one another is:

F_g = G \frac{m_1 m_2}{d^2}

where:

  • G is the gravitational constant (6.67300 × 10-11 m3 kg-1 s-2
  • m1 and m2 are the masses of the two objects attracting one another.
  • d is the distance between the two objects.

Electrical Force (Fe)

The force exerted by two electrically charged objects on one another (like a proton and an electron), is:

F_e = K \frac{q_1 q_2}{d^2}

where:

  • K is the electrical constant, sometimes called Coulumn’s constant (8.9876 × 109 N m2 C-2
  • q1 and q2 are the sizes of the charges (in Coulumbs) of the two objects attracting one another.
  • d is the distance between the two objects.

Magnetic Force (Fm)

The force exerted by two magnets on one another, is:

F_m = \mu \frac{p_1 p_2}{d^2}

where:

  • μ is a constant, (a little simplified)
  • p1 and p2 are strengths of the magnetic poles of the two objects attracting one another.
  • d is the distance between the two objects.

The magnetic force is a little more difficult to give a single equation for, because you need to factor in the shape of the magnets.

Inverse Square Laws

In addition to gravity, electric, and magnetic forces, light (which is electromagnetic radiation) and sound also obey inverse square laws.

Magnetism

Notes:

Magnetic field of a bar magnet; shown by the alignment of iron filings. Image by Black and Davis (1913) via Wikipedia.

What creates magnetic fields? (36.3)

Magnetic fields are created by moving electric charges. At the atomic level:

  • In atoms, most of the magnetic field comes from the spinning of electrons (remember electrons have a negative charge).
  • In most elements, the magnetic fields of electrons pair up and cancel each other out
  • Only certain elements, which have a few electrons that don’t pair up, can form magnets:
    • Iron (Fe), Nickel (Ni) and Cobalt (Co) are the common magnetic elements.
    • Iron is the most powerful magnetic element. It has 4 electrons whose magnetism are not canceled out (because of their arrangement in their electron shells)
    • Some rare earth elements are also naturally magnetic.

Magnetic Domains (36.4)

Each iron atom has a very small magnetic field, but when a bunch of them line up they add to each other to create a stronger field.

A region with a bunch of lined up atoms is called a magnetic domain.

Microscopic view of the grains that make up a magnet. Each grain has a magnetic field that, if oriented in the same direction, makes for a strong magnet. Each magnetic grain is called a magnetic domain. (Image by Gorchy (2005) via Wikipedia).

If all the magnetic domains line up you have a strong magnet. If they’re all randomly arranged, you don’t have a magnet at all; they cancel each other out and it’s unmagnetized).

Unmagnetized iron (left) and magnetized iron (domains aligned) (right). Adapted from image by Theresa knott at en.wikibooks.

Magnetic Poles (36.1)

Magnets have two poles: a north-seeking pole, and a south seeking pole; they align with the Earth’s magnetic field.

Like poles repel and opposite poles attract.

The force between the poles depends on the strength of the poles (p) and the distance (d) between them:

F \propto \frac{p_1 p_2}{d^2}

Note how similar this equation is to the force between two charges (Coloumb’s Law; Fc), and the force between two masses (gravitational force; Fg).

Electric fields come from charged particles, which can be separated, but north and south magnetic poles belong to each domain (and even each atom) so they cannot be separated.

  • If you break a bar magnet in half you don’t get a separate north and south poles, you just get two magnets, each with it’s own north and south pole.

Magnetic Fields (36.2)

Magnets that are free to move will align themselves with the magnetic fields around them.

The region around the magnet that is affected by the magnetic force is filled with a magnetic field. In theory the magnetic force goes on forever, but is only strong in a relatively small region.

Compasses, which have magnets that are free to move, will align themselves with the magnetic fields around them. When you’re away from other magnets and electronic devices, compasses align with the Earth’s magnetic field.

So how do you create a magnet?

In an unmagnetized piece of iron, the magnetic domains are arranged randomly. If you place it in a strong magnetic field, the domains will align with the strong magnetic field and the iron will become magnetic.

  • Softer iron alloys will align easier, and stay aligned to make strong, permanent magnets.
  • Any metal with iron in it (like steel cans or filing cabinets) will gradually align their magnetic domains with the Earth’s magnetic field if they not moved for a long time, but the Earth’s field is not strong enough to make a permanent magnet.
  • Stroking a piece of iron with a magnet will also align the domains.
  • Touching a magnet to a paperclip or iron nail will align its magnetic domains and create a temporary magnet, which is why you can use a magnet to hold up a chain of nails. This induced magnetism will only last a short time and eventually (within seconds or minutes) of removing the magnet, the nails will lose their magnetism.
  • Dropping or heating a permanent magnet will shift some of the domains out of alignment, reducing the strength of the magnet.

Where the Trees Are

Map of Woody Biomass in the U.S. in the year 2000, by the Woods Hole Research Center, via NASA's Earth Observatory.

The Woods Hole Research Center put together this map of “Aboveground Woody Biomass” that essentially shows where the trees are in the U.S.. The map was created using, primarily, satellite imagery. Their website has a nice, interactive, version of the map, and a 3d video flyover of the of southeastern Georgia.

Trees build their woody biomass using carbon from the atmosphere (remember during photosynthesis plants absorb carbon dioxide gas), so these trees are represent stored carbon. If they are burned their carbon is released to the atmosphere. If more trees are planted then they will absorb more carbon dioxide from the atmosphere. This map serves as an inventory of what we have now; a baseline for discussions about what to do about carbon-driven climate change.

The Mississippi River flood plain shows up remarkably well because of it's lack of trees. Flood plains are great for agriculture.

The Magnetic Fields of the Planets

The Earth’s magnetic field results from the movement of molten metal in the Earth’s core. The outer core actually. It’s mostly molten iron, which conducts electricity, and as it convects up and down, like boiling water in a pot, the moving electrical charges create the Earth’s magnetic field. Its a bit like a dynamo.

The internal structure of the Earth. Movement in the liquid metal outer core (green arrows) generates the earth's magnetic field.

What drives the convection of the outer core? The heat released from the freezing of the liquid metal to the solid inner core. The inner core is ever expanding, and the outer core is getting smaller and smaller. Ultimately, when the entire outer core freezes the Earth’s magnetic field should disappear. But we’ve got some hundreds of millions of years left so we don’t have to worry quite yet.

The Other Planets

The question came up: Do Mars and the other planets have magnetic fields?

Astronomynotes has compiled a table of Planet Atmospheres and Magnetic Fields that shows that of the inner planets — Mercury, Venus, Earth and Mars — only the Earth has a significant magnetic field; Mercury does have its own field but it has less than 1% the strength of the Earth’s.

At present, Mars does not have a magnetic field, but it does have remnant magnetism imprinted on its rocks, indicating that it used to have one in the past. It’s internal dynamo died away long ago. Interestingly, the pattern of Mars’ remnant magnetism indicates that it’s interior was once molten enough that the surface had tectonic plates just like the Earth.

Comparison of Earth's healthy magnetic field and the local, remnant magnetism of Mars. Image via NASA.

On the other hand, the outer planets have much larger magnetic fields; Jupiter’s is almost 20 times larger than Earth’s. The gas giants’ magnetic fields are also generated by fluid motion in their interiors (Stevenson, 1983 (pdf)). It’s likely, however, that in some of these bigger planets, at least, the electrically conductive fluid is not liquid metal like in the Earth’s core, but either liquid hydrogen, or a water solution with dissolved electrolytes.

Jupiter's strong magnetic field interacts dramatically with its moons, inducing magnetic fields in some. Image via NASA.

Drawings of Jupiter

Étienne Trouvelot's drawing of the planet Jupiter from 1880 (via the New York Public Library), combined with an image of the planet from the Cassini spacecraft taken in 2000 (NASA/JPL/Space Science Institute)

The New York Public Library’s website hosts a remarkable collection of Étienne Léopold Trouvelot‘s astronomical drawings by that date back to 19th century.

The beauty and detail of these illustrations are a remarkable testament to the intersection of art and science.

Mare Humorum. From a study mad... Digital ID: TROUVELOT_006. New York Public Library

Building a Simple Electric Motor

This is a really simple electric motor that only requires some wire, a battery, and a magnet. Simon Quellen Field has a wonderfully detailed description of how to build the motor, and some elegant tips on how you can make the motor run faster.

My middle-schoolers quite enjoyed building one of these, and I’m planning on having my high-school physics students also try it; only a couple of them claim to have done it before. It should be a good way to tie together electricity and magnetism.

(Evil Mad Scientist has an even simpler motor, but, given that the risk that their homopolar motor is quite capable of launching a drywall nail across the room, I think I’d suggest not trying that one without extremely close supervision.)

Although it’s a bit trickier, another great way of demonstrating electromagnetic induction is to build a simple alternating current generator that runs a small light bulb.

Bill Beaty’s website explains how to build the generator in excellent detail.

The best part of building the generator is that you can actually feel the extra energy it takes to light the bulb, as you spin the magnets.

Impressions of Monet

Nympheas, by Claude Monet. Image via Wikipedia.

We took the middle and high school to see the Monet Water Lilies exhibit at the St. Louis Art Museum today. It was a nice tour; we saw some paintings, and we learned a little something about the impressionists.

One thought that occurred to me during an interesting conversation on the bus back to school, was how the development of abstract thinking skills affects our perception of the more abstract art. After all, it usually requires more effort to appreciate, understand and become affected a piece the more abstract it is. Which would suggest that art appreciation would be useful practice for adolescents who are honing their higher-level cognitive skills.

The tour also left me with one unanswered question, however: are we seeing fog or smog in Monet’s painting of the Charing Cross Bridge in London.

Charing Cross Bridge by Monet. Image via Wikipedia.

London is famous for its fogs, but this painting was done in 1899, well into the industrial revolution, and the yellow tints suggest a pea-souper.