A magnet is an object made of certain materials which create a magnetic field.  Every magnet has at least one north pole and one south pole.  By convention we say that the magnetic field lines leave the North end of a magnet and enter the South end of a magnet.  This is an example of a magnetic dipole ("di" means two thus two poles).  If you take a bar magnet and break it into two pieces each piece will again have a North pole and a South pole.  If you take one of those pieces and break it into two each of the smaller pieces will have a North pole and a South pole.  No matter how small the pieces of the magnet become each piece will have a North pole and a South pole.  It has not been shown to be possible to end up with a single North pole or a single South pole which is a monopole ("mono" means one or single thus one pole).

Ferromagnetism
When a ferromagnetic material is placed near a magnet it will be attracted toward the region of greater  magnetic field.  This is what we are most familiar with when our magnet picks up a bunch of paperclips.  Iron cobalt nickel gadolinium dysprosium and alloys containing these elements exhibit ferromagnetism because of the way the electron spins within one atom interact with those of nearby atoms.   They will align themselves creating magnetic domains forming a temporary magnet.   If a piece of iron is placed within a strong magnetic field the domains in line with the field will grow in size as the domains perpendicular to the field will shrink in size. 

Diamagnetism
When a diamagnetic material is placed near a magnet it will be repelled from the region of greater magnetic field just opposite to a ferromagnetic material.  It is exhibited by all common materials but is very weak.    Metals such as bismuth copper gold silver and lead as well as many nonmetals such as graphite water and most organic compounds are diamagnetic.

Paramagnetism
When a paramagnetic material is placed near a magnet it will be attracted to the region of greater magnetic field like a ferromagnetic material.  The difference is that the attraction is weak.  It is exhibited by materials containing transition elements rare earth elements and actinide elements.  Liquid oxygen and aluminum are examples of paramagnetic materials. 

The fact about Magnets
1. North poles point north south poles point south.
2. Like poles repel unlike poles attract.
3. Magnetic forces attract only magnetic materials.
4. Magnetic forces act at a distance.
5. While magnetized temporary magnets act like permanent magnets.
6. A coil of wire with an electric current flowing through it becomes a magnet.
7. Putting iron inside a current-carrying coil increases the strength of the electromagnet.
8. A changing magnetic field induces an electric current in a conductor.
9. A charged particle experiences no magnetic force when moving parallel to a magnetic field but when it is moving perpendicular to the field it experiences a force perpendicular to both the field and the direction of motion.
10. A current-carrying wire in a perpendicular magnetic field experiences a force in a direction perpendicular to both the wire and the field.
 
The types of magnets
There are three main types of magnets:
    Permanent magnets
    Temporary magnets
    Electromagnets
Permanent Magnets
Permanent magnets are those we are most familiar with such as the magnets hanging onto our refrigerator doors.  They are permanent in the sense that once they are magnetized they retain a level of magnetism.  As we will see different types of permanent magnets have different characteristics or properties concerning how easily they can be demagnetized how strong they can be how their strength varies with temperature and so on.

Temporary Magnets
Temporary magnets are those which act like a permanent magnet when they are within a strong magnetic field but lose their magnetism when the magnetic field disappears.  Examples would be paperclips and nails and other soft iron items.

Electromagnets
An electromagnet is a tightly wound helical coil of wire usually with an iron core which acts like a permanent magnet when current is flowing in the wire.  The strength and polarity of the magnetic field created by the electromagnet are adjustable by changing the magnitude of the current flowing through the wire and by changing the direction of the current flow.
Materials used for permanent magnets
There are four classes of permanent magnets:
    Neodymium Iron Boron (NdFeB )
    Samarium Cobalt (SmCo)
    AlNiCo
    Ceramic or Ferrite
This table gives us some of the special characteristics of the four classes of magnets. 
Br is the measure of its residual magnetic flux density in Gauss which is the maximum flux the magnet is able to produce.   ( 1Gauss is like 6.45 lines/sq in)
Hc is the measure of the coercive magnetic field strength in Oersted or the point at which the magnet becomes demagnetized by an external field.  ( 1Oersted is like 2.02 ampere-turns/inch)
BHmax is a term of overall energy density.  The higher the number the more powerful the magnet.
Tcoef of Br is the temperature coefficient of Br in terms of % per degree Centigrade.  This tells you how the magnetic flux changes with respect to temperature.  -0.20 means that if the temperature increases by 100 degrees Centigrade its magnetic flux will decrease by 20%!
Tmax is the maximum temperature the magnet should be operated at.   After the temperature drops below this value it will still behave as it did before it reached that temperature (it is recoverable).  (degrees Centigrade)
Tcurie is the Curie temperature at which the magnet will become demagnetized.  After the temperature drops below this value it will not behave as it did before it reached that temperature.  If the magnet is heated between Tmax and Tcurie it will recover somewhat but not fully (it is not recoverable). 
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Both the NdFeB and the SmCo magnets are generally known as rare earth magnets since their compounds come from the rare earth or Lanthanide series of the periodic table of the elements.  They were developed in the 1970's and 1980's.  As can be seen in the table these are the strongest of the permanent magnets and are difficult to demagnetize.  However the Tmax for NdFeB is the lowest.
AlNiCo magnet is made of a compound of aluminum nickel and cobalt.  AlNiCo magnets were first developed in the 1940's.  As can be seen in the table this magnet is least affected by temperature but is easily demagnetized.  This is the reason why bar magnets and horseshoe magnets made of AlNiCo will easily become demagnetized by other magnets by dropping it and by not storing it with a keeper.   Its Tmax though is the highest.
Ferrite magnets are the most popular types of magnets available today.  The flexible magnets we use are a type of ferrite magnet with the magnetic powders fixed in a flexible binder.  These were first developed in the 1960's.  This is a fairly strong magnet not as easy to demagnetize as AlNiCo but its magnetic strength will vary the most as its temperature changes. 

Shapes
Permanent magnets can be made in most any shape imaginable.  They can be made into round bars rectangular bars horseshoes rings or donuts disks rectangles multi-fingered rings and other custom shapes.  Some are cast into a mold and require grinding to achieve final dimensions.  Others start as a powder which is pressed into a mold or pressure bonded or sintered.
How are magnets made?
There are 6 basic steps to making a magnet such as a Neodymium Iron Boron magnet = Nd2Fe14B or Nd15Fe77B8.
1.  Make an alloy of iron boron and neodymium.  You will need about 14 grams of boron and 369 grams of neodymium for every 1000 grams of iron to make an alloy of Nd2Fe14B.  This will have to be heated above 1538 degrees Centigrade to make it melt.  The mixing of the materials with the iron is very important just like thoroughly mixing the ingredients for a cake.
2.  Grind the alloy into a powder.  After the alloy has cooled you will need to grind it or mill it into a very fine powder.
3.  Compress the powder into a shape.  Since the magnet will have a specific shape when you are done you use a mold of that shape to make the magnet.  For example you may want a disk.  Pour the powder into a mold that has a disk shape but is also deeper than the thickness of the final part.  Next you will compress the powder with hundreds of pounds of pressure to compact the powder into a solid disk.  Heat is often used to help fuse the particles together and is called a sintered magnet.  Sometimes a glue is used to help keep it all together and is considered to be a bonded magnet.  To achieve precise final dimensions you may need to grind the part.
4.  Coat the magnet.  In order to improve the corrosion resistance of the magnet the disk needs to be plated with a thin film of nickel.  Sometimes a film of gold is used or zinc or an epoxy coating..  Nickel does not oxidize like iron so it works great for magnets you will be touching.
5.  Magnetize the magnet.  All this time the powder and the disk is not magnetized.  It would be attracted to and stick to a magnet but it would not be able to pick up a paper clip all by itself.  So it would be placed into a magnetizing fixture that has a coil of wire through which a very large pulse of current is passed for a very short period of time.  The magnet has to be held in place so it doesn't shoot out and hit something or someone.  It takes about a thousandth of a second to actually  magnetize the magnet.  
6.  Pack and ship it.  You now have a magnet for whatever you need.  Engineers often require special shapes or specific magnetization configurations to make the product they are designing work properly.  They talk with the magnet manufacturer and they determine how to best make the magnet that is needed.  That's why there are so many different shapes and sizes of magnets in the catalogs.
Magnetization configurations
How the magnet is magnetized is as important as its shape.  For example a segment magnet can be magnetized where N is on the inside and S on the outside or N is on one edge and S on the opposite edge or N is on the top side and S on the bottom side or multiple N and S poles all around the outside edge etc.   A big help in visualizing how a magnet may be magnetized is by using a magnetic viewing film.  Obtain one of these viewing cards and look at the magnets you have around your house.  The white line marks the boundary between the N and S poles.  Make a sketch of what each magnet looks like under the viewing film.  You will be surprised by some. 

What affects the strength of a magnet?
Material
As seen in the previous section the material the permanent magnet is made from has a significant effect on the overall strength of a magnet.  The material will also determine how its flux is affected by temperature and how easily the magnet can be demagnetized by opposing magnetic fields.
Temperature
The temperature coefficient column indicates how the magnetic flux varies with the temperature of the magnet. 
Demagnetizing fields
The Hc column in the data table above indicates the strength of a magnetic field which can demagnetize a magnet.  The magnet would have to be subjected to it in an opposing or repelling manner. 
Physical impact
Magnets can become demagnetized by physically hammering or dropping them when the poles of the magnet are opposite to the poles of the earth or at right angles to the poles of the earth.  Steel nails can also become magnetized when hammered when the nail is lined up with the poles of the earth.
 
The Care and Feeding of your Magnet
How do you take proper care of your permanent magnet?  
There are only four areas you need to be concerned with:
a.    Mechanical Shock
b.    Heat
c.    Moisture
d.    Demagnetizing Fields
Depending on the class of magnet you have the care will vary slightly. 
 
Ferrite Magnets

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They are usually black or dark gray in color but the surface may be painted any bright color.  These also include the flexible magnets since the flexible binder has magnetized ferrite material in it.
A.  Mechanical Shock
These magnets are brittle - they will chip or crack or break easily when:
            dropped onto a hard surface
            allowed to smash together with another magnet
            allowed to smash together with a piece of metal
            struck with a hammer or other hard substance
So handle gently like you do with your iPod or cell phone.  When you bring two magnets together be prepared to have the force of attraction increase quickly and dramatically as the North pole of one gets closer to the South pole of the other.  Better still place a plastic disk or rubber washer between them so there is a cushion between them.  Watch your fingers so they don't get pinched!
You may not realize it but every particle within a magnet wants to push away from every other particle next to it.  Yes it is attracted to the particle at its North end and South end but all along its sides there is a repulsion.  Because of this if two magnets are allowed to smash together expect a small chip or particle to fly away at a high velocity and can fly into your eye.  That is why it's a good thing to wear goggles - protect your eyes from the unexpected.  Those particles have sharp edges and will easily scratch your eyes.
B.  Heat
As the temperature increases the molecules that make up the magnetic material with their poles all lined up will start to wiggle and jiggle around causing the strength of the magnet to decrease.  If allowed to go above their maximum working temperature they will lose some of their strength and will not be able to recover it when it cools back down.  If allowed to go above their Curie Temperature they will lose all of their magnetic strength and will not be able to recover from it.
For ferrite and ferrite magnets their maximum working temperature is 300 degrees C . 
The maximum working temperature for flexible magnets is about 180C.
The Curie Temperature for ferrite and ferrite magnets is 460C .
C.    Moisture
Ferrite magnets do not corrode or rust easily so you don't have to worry too much about them.
D.    Demagnetizing Fields
Ferrite or ferrite magnets are fairly rugged regarding their resistance to be demagnetized.  This is true as long as you keep them away from rare earth magnets.  But when used with other ferrite magnets there is little chance of demagnetizing them even if you store them with North and North poles touching.

AlNiCo Magnets

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AlNiCo magnets are the magnets you usually play with at school in horseshoe shapes and as bar magnets.  They have a color like aluminum and are also usually painted red or black or left with its natural color.  
A.  Mechanical Shock
These magnets are very tough - they do not chip or crack or break easily when:
            dropped onto a hard surface
            allowed to smash together with another AlNiCo magnet
            allowed to smash together with a piece of metal
            struck with a hammer or other hard substance
You still have to be prepared to have the force of attraction increase quickly and dramatically as the North pole of one gets closer to the South pole of the other.  Magnets made of AlNiCo are usually cast in a mold and then magnetized.
B.  Heat
Heat is another strength for AlNiCo magnets.
Their maximum working temperature is 540 degrees C .
The Curie Temperature for AlNiCo magnets is a blistering 860C .
Hot temperatures are not going to affect these magnets much!
C.    Moisture
Again with the aluminum and nickel mixed in the alloy with the iron AlNiCo magnets are not prone to rusting or corroding.  So they work great in tough environments.
D.    Demagnetizing Fields
The weakness of AlNiCo magnets is that they can easily be demagnetized - even with another AlNiCo magnet.  They don't last long when you push two North poles together to feel the repulsion.  After a while you will notice that they begin to weaken.  The greatest care for these magnets is in how you store them and restore them.
First you don't want to bring ferrite or rare earth magnets close to AlNiCo magnets.  You can very quickly demagnetize them or remagnetize them in the opposite direction!  How should they be stored?
If you have a horseshoe AlNiCo magnet store them with a keeper.  This is just a steel bar that will stick to the two ends of the magnet.  The purpose is to allow the field to continue flowing through the horseshoe and not be pushed around by other magnetic fields.  The following diagrams show this.  You could even place two horseshoes together with opposite poles touching to keep them strong.
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If you have bar magnets they can be stored in pairs or back to back with opposite poles touching.  Or if you only have one place it onto a steel sheet that would act like a big keeper.  These diagrams show this.
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If and when they become weak they can be restored using a remagnetizer. Inside of a remagnetizer are some very strong rare earth magnets that will re-align the domains in the AlNiCo so that they will be as good as new again.

SmCo Magnets

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SmCo magnets are not seen very often.  They are used in small motors for your VCR or your CD / DVD player.  They are more expensive than the other magnets but with a special set of strengths.
A.  Mechanical Shock
These magnets are brittle - they will chip or crack or break easily when:
            dropped onto a hard surface
            allowed to smash together with another magnet
            allowed to smash together with a piece of metal
            struck with a hammer or other hard substance
So again handle gently like you do with your iPod or cell phone.  When you bring two magnets together be prepared to have the force of attraction increase quickly and dramatically as the North pole of one gets closer to the South pole of the other.  Better still place a plastic disk or rubber washer between them so there is a cushion between them.  Watch your fingers so they don't get pinched!
You may not realize it but every particle within a magnet wants to push away from every other particle next to it.  Yes it is attracted to the particle at its North end and South end but all along its sides there is a repulsion.  Because of this if two magnets are allowed to smash together expect a small chip or particle to fly away at a high velocity and can fly into your eye.  That is why it's a good thing to wear goggles - protect your eyes from the unexpected.  Those particles have sharp edges and will easily scratch your eyes.
B.  Heat
For a very strong magnet these can handle a fair amount of heat.
Their maximum working temperature is 300 degrees C .  
The Curie Temperature for SmCo magnets is 750C .
Very respectable for a sintered magnet. 
C.    Moisture
Rust and corrosion from water is not a big factor with SmCo magnets.  They can survive in a fairly tough environment.
D.    Demagnetizing Fields
About the only thing that can demagnetize a SmCo magnet is a NdFeB magnet.  So for storage keep them separate from other classes of magnet for two reasons:  1.  they don't demagnetize other weaker magnets and 2. so they aren't demagnetized by stronger magnets.

NdFeB Magnets

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NdFeB magnets are the strongest permanent magnets around today and are not very expensive.  They are used in headphones disk drives new toys all over the place.
A.  Mechanical Shock
These magnets are brittle - they will chip or crack or break easily when:
            dropped onto a hard surface
            allowed to smash together with another magnet
            allowed to smash together with a piece of metal
            struck with a hammer or other hard substance
So again handle gently like you do with your iPod or cell phone.  When you bring two magnets together be prepared to have the force of attraction increase quickly and dramatically as the North pole of one gets closer to the South pole of the other.  Better still place a plastic disk or rubber washer between them so there is a cushion between them.  Watch your fingers so they don't get pinched!  Because these magnets are so much stronger than others this needs to be a real precaution!
You may not realize it but every particle within a magnet wants to push away from every other particle next to it.  Yes it is attracted to the particle at its North end and South end but all along its sides there is a repulsion.  Because of this if two magnets are allowed to smash together expect a small chip or particle to fly away at a high velocity and can fly into your eye.  That is why it's a good thing to wear goggles - protect your eyes from the unexpected.  Those particles have sharp edges and will easily scratch your eyes.
B.  Heat
This is the weakness of this magnet.  
Their maximum working temperature is only 180 degrees C .  
The Curie Temperature for NdFeB magnets is 310C .
This is why they usually aren't used in motors.  Keep your magnets cool.  
C.    Moisture
This is another area of weakness.  To combat the problem of these magnets corroding so easily they are usually coated or plated.  A popular plating material is zinc since it is cheap but it isn't very good.  A better coating is nickel.  This keeps them looking nice and shiny for a long time.  Some are coated with a very thin layer of gold over the nickel.  This is more for looks but is also useful since gold does not tarnish.
D.    Demagnetizing Fields
This is an area where these magnets outperform others.  They are tough to demagnetize.  This also means that they can easily demagnetize other classes of magnets - like SmCo or AlNiCo or Ferrite!  Again store your magnets separately by class.
Storage of Magnets
Basically store different classes of magnets separately.  Keep your ferrites together in one place your AlNiCo in another (away from the ferrites) your SmCo in still another location and your NdFeB magnets by themselves.  This is the biggest rule for storage - putting distance between the various classes of magnets.
What do I do with them after they are separated into their classes?  
Ferrite magnets should be stacked North to South with others their same size.  When you have  a really long stack start another stack.  These stacks can sit side by side in a drawer or box.  You may want to place them in plastic bags or wrap them in paper towels to keep the drawer clean - otherwise the drawer surface starts to take on a gray color.
AlNiCo magnets should be kept in their own drawer or box.  Remember their keepers for the horseshoes and remember to stick pairs together or place a steel bar alongside the bar magnets.  Other magnets can easily demagnetize them.  See the photos above for AlNiCo magnets.
If you have SmCo magnets keep them in their own drawer or box.  Stack them with a separator between them to make it easier to slide them apart when you want just one.
NdFeB magnets can be jumbled together really but if you do this they will be very difficult to separate from each other.  It would be neater to place them in groups of similar shapes.  For magnets that are larger than 1/2" on a face place a plastic disk or sheet as a separator between each magnet to make it easier to slide them apart.  Wrap groups of them in a paper towel or place them in plastic bags so the groups can be easily separated.  I keep my spherical Neodymium Iron Boron magnets in tennis balls so I don't hurt myself and they don't whack into each other destroying themselves.  
Isolating Magnets
What if you want to keep stray magnetic fields to a minimum?  Having magnets in a drawer or box isn't too bad since the strength decreases with the square of the distance.  It decreases quickly.  If you really want to isolate the magnetic field created by the permanent magnets you will need to make a steel cage or box to keep them in.  Here are some ideas.  
Having a stack of magnets will produce a large stray field. Placing a stack of magnets onto a steel bar or plate helps contain some of the field. Placing 2 3 or 4 steel bars around the stack of magnets does a good job of containing the magnetic field.  
Sticking steel end pieces onto the stack of magnets further directs the field into the bar and not allow it to stray.
Sticking multiple bars around the magnets with steel end pieces takes this a step further.  There is very little stray field with this arrangement.  
Place half the stack of magnets onto a steel plate and place the other half turned around onto the same plate and add a second plate on top.  So each plate is seeing a North pole from one stack and a South pole from the other stack.  The steel plate is acting like a low resistance path for the magnetic field to from one stack to the other.  Think of this as shorting out the magnet - but this does not damage the magnet in any way!
Placing any of the above into a steel container will prevent the field from going outside the steel container.  This can be something like a paint can or soup can.
The best you can do is to place the magnets into a thick steel container with space between the magnets and the inside walls.
When shipping magnets the field outside the shipping carton needs to be below a certain level.  This is often achieved by: 
1.    wrapping the magnet(s) in foam
2.    placing it in a plastic bag
3.    placing the bag into a steel can with foam between the bag and the inside walls of the can
4.    placing the can into a cardboard box with styrofoam packing surrounding the can to keep it in the middle of the box
If you have the gaussmeter you can check to see how weak the field outside the box is.  Make this an experiment to determine the most cost effective solution to achieving a method of storing magnets with very low stray fields.
To goal is to contain the field.  The best way to do this is to provide an easy path for the magnetic field to go from the North pole to the South pole.  If you do that the field won't want to go anywhere else!  You direct it where you want it.