Does the size of the magnet make it stronger? How are magnets made? How does the shape of a magnet effect it's magnetic field?
Size is just one of the ways one can change the strength of a magnet. However, it can get very difficult and expensive to simply make a magnet bigger. The other way is to make it BETTER. This can mean all sorts of things. With electromagnets, the modern method to make them better is to construct a superconducting magnet. That is, the electrical coils are made of materials that will lose all electrical resistance when immersed in a tremendously cold substance, such as liquid helium. Jefferson Lab has lots of liquid helium just for the purpose of attaining superconductivity, although most of it is not for magnets but for the accelerator's niobium cavities. However, the point is still the same. By reducing the electrical resistance, much higher amounts of electrical current can be put through the magnets, thereby generating a much stronger magnetic force.
Another way to make a magnet better is by carefully choosing the material from which it is made. The standard strong magnet found in labs is usually made from ALNICO - a special alloy where strongly magnetic bits, made from an iron-nickel-aluminum alloy are embedded in an iron-cobalt alloy base. If you want something lighter that can generate a strong magnetic force, then one can try FERRITE (or ceramic) magnets which are made from iron oxide plus barium, strontium, or lead oxide. Like other ceramic materials (such as toilet bowls), they are brittle, so some care in handling is necessary. If you want to look over some varieties of permanent magnets, you can check out the online Edmund Scientific catalog. The strongest permanent magnets are made from an iron-neodymium-boron (Fe-Nd-B) alloy. This kind is actually used as a critical part of a nuclear physics experiment called the Alpha Magnetic Spectrometer (AMS). Almost without exception, nuclear physics experiments require a strong magnet and it is often a superconducting one. The AMS was designed as a compact system capable of being launched into space aboard the space shuttle. The standard nuclear physics electromagnet was out of the question. With the new type of permanent magnet made from the Fe-Nd-B alloy, the required strong magnetic field could be attained in a very compact volume without using any electrical power or liquid helium.
The details of manufacturing permanent magnets are proprietary (i.e., a trade secret). However, the general technique is to take a FERROMAGNETIC material such as the ALNICO and expose it to a strong magnetic field, probably generated as very short (on a time scale) but very powerful bursts from a nearby electromagnet. The magnetic "bits" in a ferromagnet are small collections of material (say, a millimeter or so) called domains that have a definite magnetic field with a north and south pole. Normally, these domains are oriented in random directions, thereby canceling each other out. When exposed to this powerful outside field, the domains start to orient themselves according to the direction of the strong outside field. The newer Fe-Nd-B alloy magnets have the added advantage that after the field is established, it tends to be more stable than other types of permanent magnets.
Carl Zorn, Detector Scientist (Other answers by Carl Zorn)