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## 1. Electric Fields and Magnetic Fields

Electric fields are often associated with stationary electric charges, and magnetic fields with moving electric charges. Whether an electric charge is stationary or moving depends on how the charge and the observer move relative to each other, so different observers at (nearly) the same location can measure different electric and magnetic fields, if those observers have different relative motions. It is therefore customary to view electric fields and magnetic fields as different aspects of a combined field, which is called the electromagnetic field.

A variation in an electric field can cause a magnetic field, and a variation in a magnetic field can cause an electric field. Electromagnetic radiation such as visible light or radio waves or X-rays are infinite loops of a tiny magnetic field causing a tiny electric field causing a tiny magnetic field, and so on, without any electric charge being needed.



## 2. Compasses

A compass is a device that shows the horizontal direction of the magnetic field. A compass usually has a compass needle that is balanced in the middle on a small vertical pen so that the needle can rotate freely and can orient itself to the magnetic field.

A compass needle always extends in two directions and orients itself to invisible magnetic field lines that run straight from the northern magnetic pole of the Earth (also called the northern geomagnetic pole) to the southern magnetic pole of the Earth (the southern geomagnetic pole). Of the two ends of a compass needle, one points along the magnetic field line to the northern magnetic pole and the other one to the southern magnetic pole. The end that points to the northern magnetic pole is usually painted red.

The northern magnetic pole of the Earth lies in northern Canada at aboout 1000 km from the geographical North Pole (which is the "real" North Pole where the rotation axis of the Earth meets the surface), and the southern magnetic pole lies near the coast of Antarctica, about 2500 km from the geographical South Pole (where the rotation axis meets the surface, too). Maps of those areas often indicate where the magnetic poles are.

Because the magnetic poles are far from the geographic poles, a compass hardly anywhere points exactly north and south. The difference between the direction to the North Pole and the direction that the compass shows is called the magnetic declination and this is different for every spot on Earth. Topographic (very detailed) maps often show what the magnetic declination of the displayed area is. In the Netherlands and Belgium the magnetic declination happens to be rather small, less than 10 degrees, but in other places it is greater, especially near the magnetic poles.



## 3. Ejection of Matter

Some celestial objects (such as T Tauri stars) eject matter, and that matter usually moves along the rotation axis (as if the matter came out of the poles). I suspect that magnetic fields are the cause of this preference.

The matter that gets ejected is so hot that it is a plasma. A plasma is like a gas, but is made up of unbound electrically charged particles (usually these are negatively charged electrons and positively charged protons) that in a gas would be tied together into atoms. A plasma is electrically neutral on large scales (just like a gas), because it contains (just like a gas) the same amount of positive charge and of negative charge, but in a plasma the particles usually move freely relative to each other (unlike in a gas). That means that a plasma is a very good conductor of electrical current, unlike a gas. And that means that a plasma is very sensitive to magnetic fields, unlike a gas.

Magnetic fields have a preferred direction (the direction of the so-called "field lines"). Electrically charged particles run in circles around those field lines, so they can move great distances along the field lines but cannot move away from the field lines. This means that electrically charged particles can only move great distances from their source along magnetic field lines, which is only possible if those magnetic fields lines themselves reach that far from the source of the particles.

Most magnetic fields of celestial objects have roughly the structure of a dipole, with a magnetic axis of symmetry: If you rotate the object around that axis over an arbitrary angle, then the magnetic field still looks roughly the same. In most celestial objects the magnetic axis is close to the rotation axis, because the rotation axis influences (through the centrifugal force) the motion of matter in or around the object, and the magnetic field is tied to the motion of matter in or around the object. In the Earth, too, you can recognize the rotation axis by looking at the shape of the object: the Earth's diameter is smaller from pole to pole than it is through the equator. And the Earth's magnetic axis is close to its rotation axis.

Electrical field lines begin on positive electrical charge and end on negative electrical charge. Magnetic field lines must always be closed (have no beginning or end), because there isn't such a thing as a "magnetic charge". So, every field line that pierces the surface of an object upward must eventually turn around and pierce the surface again going down. Because of symmetry, the "return points" must lie roughly about the magnetic equator, so only magnetic field lines that run very close to the magnetic axis can get very far from the object, so only plasma that runs very close to the magnetic axis can get very far from the object. This explains in many cases why matter preferentially moves away from hot objects from the polar regions.

The other way around, plasma particles from far away can get closest to a celestial object if they approach that object near one of its poles. That is the reason why the Earth has polar lights, and not also "equatorial lights": only near the magnetic poles can electrically charged particles from far away reach the top layers of the Earth's atmosphere.



### 3.1. Electrons and Magnetic Field Lines

Electrons are diverted by magnetic fields. If the magnetic field is equally strong everywhere then the electrons will move in circles around the field lines (or in corkscrew orbits if they also have a speed along the magnetic field lines). The radius of the circles depends on the speed of the electron (the faster the electron, the greater the radius) and on the strength of the magnetic field (the stronger the field, the smaller the radius):

\begin{equation} r = \frac{m v}{q B} \end{equation}

where $$r$$ is the radius of the circular orbit, $$m$$ the mass of the electron, $$v$$ the speed of the electron measured at right angles to the direction of the magnetic field, and $$B$$ is the strength of the magnetic field.

So, electrons cannot move arbitrarily far from the field lines, so you might say that (as seen from large distances) they move along the field lines.

Photons are not influenced by magnetic fields.



### 3.2. Permanent Magnets and Energy

A permanent magnet needs no energy to maintain its magnetic field. Magnetism is a property, just like electrical charge or mass, that doesn't just leak away. Changes in energy follow when objects move under the influence of the magnetic field.

Radioactive substances decay because that does not cost energy but rather frees up energy. If no more energy can be freed, then they don't change any more, except perhaps if energy is delivered from outside. It works the same way for gravity: a ball on a slope has a tendency to roll downward, because that frees up energy. You have to do work to get a ball up the slope, so a ball higher up the slope has more (gravitational) energy than a ball lower down the slope. The ball on the slope only starts rolling downhill if it isn't accidentally lying inside a dimple on the slope, because if it is in such a dimple then it needs a little push (extra energy) to get over the edge of the dimple, because then it goes against the force of gravity. If the ball is in such a dimple, then you have to wait for a gust of wind or a kick from a child before the ball starts rolling down the hill. Radioactivity works in a similar way. Radioactive particles are (energetically speaking) in a "dimple" on a "hill". To stay in the same metaphor, only if there is a sufficiently strong gust of wind can it get out of the dimple and roll downhill: then the radioactive particle decays (radioactively).

If two magnets are brought close together, then it is as if you place them in a hilly country of magnetic energy, where the placement and orientation of the hills depends on the orientation and relative placement of the magnets. If the two magnets are on slopes in that magnetic landscape, and if there isn't much friction (dimples), then they tend to move downhill. In the "real" world this may correspond to them moving closer together (attraction), or move further apart (repulsion), or rotate.

An electromagnet has a magnetic field because of the electrical current that flows through the magnet. If that current stops, then the magnetic field disappears. A permanent magnet has a magnetic field because of the properties of the material. As long as those properties don't change (for example due to heating or by applying another strong magnetic field), the magnetic field stays intact.

If objects move under the influence of a permanent magnetic field, then the energy that is required to make the objects move comes from the cause of the current situation. If you move the object close to the magnet, then you have to overcome any magnetic forces that want to move the object somewhere else. You are then the source of the energy that is needed to later make the object move where the magnet wants it to go. This works the same as for other forces, such as gravity: if you want to make a ball move under the influence of gravity (i.e., downward), then you first have to move the ball against the force of gravity (i.e., upward), which means you have to spend energy. You've put that energy into the ball in the form of "energy of location" (physicists call this "potential energy"), which gets transformed into "energy of motion" ("kinetic energy") if you let go of the ball in its high position.

There is no fundamental difference between magnetic and electric fields that are generated by an electromagnet and the fields that are generated by a permanent magnet. All of them are described by the Laws of Maxwell. languages: [en] [nl]

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Last updated: 2017-04-24