Lecture Videos

• Charges positive and negative from last week
• As the distance that separated the two charges increases, the force decreases dramatically
• Instead of positive and negative charges, there are the north and south ends of the magnets
• North and south magnets attract each other
• As the distance that separated the two magnets increases, the force decreases dramatically
• Main difference between electricity and magnets, there are no magnetic monopoles
• North and south of magnets always tied together. So when broken, new opposite ends form
• Why are poles tied together?

  Magnetism comes from tiny (quantum) motion of electric charges
• North and south effectively give the direction of magnetic field lines
• Fields tell us the force that something would feel in the location of the field
• Why use fields now?


  Because we cannot separate north and south poles
• Rules:

  • outside magnet: lines go from north to south, inside magnet: lines go from south to north
  • Lines never cross
  • Higher line density equals a stronger field and more force
• Lines make loops around magnets
• Magnets tend to align with each other
• North of Earth is the magnetic south of Earth
• Ferromagnetic materials, some materials (commonly iron) are sensitive to magnetic fields

  Why?

  Atomic structure, each atomy becomes its own tiny magnet
• Iron from the ground usually not magnetic because all of its magnetic domains are aligned randomly
• Apply strong external field and it will become aligned
• After external field and alignment is complete, the piece becomes a permanent magnet
• Permanent magnet not actually permanent
• Magnet unaligned by heat, hit it hard, apply alternating magnetic fields
• So in lecture we got pretty deep into permanent magnets, but we didn't quite get into why they exist! There are several layers to it but I think it makes the most sense to build up to the macroscopic object that we call a "magnet" from the smallest possible piece: the electron.
• A new particle property that we can introduce regarding electrons is called "spin." Spin describes the natural magnetic field produced by an electron, and in most cases we describe this spin as "up" or "down." The terms "up" and "down" don't have any real meaning except to say that one spin is the opposite of the other. To answer the question of why they have spin is a very hard thing, but right now the answer is "because (angular) momentum conserves."
• Suppose you have an atom that has a bunch of electrons, and also suppose that the atom has 15 spin up electrons and 11 spin down electrons. Since ups and downs cancel each other out, it is left with a net of 4 spin up electrons. That atom then basically has 4 little magnets that are all agreeing with each other on the direction of their magnetic field. That atom is magnetic.
• It is actually much more likely that all of those atoms will face in random directions, with none of their magnetic fields agreeing- resulting in all of the magnetic fields cancelling out on average. This is a material called "paramagnetic." This one is common because it's just sort of a random alignment: the atoms got stuck that way and that's it.
• If you accumulate a bunch of those atoms, then you can accumulate a bunch of magnets, making for a stronger magnetic field right? Well, yeah, so long as they all agree on which way "up" is! 
• Another common alignment is when atoms agree to cancel each other out. One atom points its magnetic field left, the next one points right, and so on. This type of material is very common and is called "anti-ferromagnetic." It is common because this is the lowest energy state (in terms of these little magnets) and is very stable.
• Less common are materials that are ferromagnetic. Ferromagnetic materials are the ones where those atoms will start to agree with their neighbors on which direction to point their magnetic fields.
• The problem, however, is that they will often start out randomly oriented. As little atoms start to agree with their immediate neighbors on which direction to point, they create neighborhoods all pointing in the same direction. These neighborhoods of atoms pointing in the same direction are called "domains," and much like neighborhoods in real life, they don't necessarily agree with the next neighborhood over.
• So you end up with a large chunk of material like iron (that's where the name "ferromagnetic" comes from!) that basically has a bunch of domains (small magnets) inside of it that are not agreeing on which direction to point. Also, each of those domains are made of a bunch of smaller magnets (iron atoms) that do agree on which way to point.
• The bigger a domain gets, the harder it will be to change it's direction, think about turning a small sedan around compared to making a u-turn in a tractor-trailer. So how do we force these domains to align? You expose them to a stronger external magnetic field- much like ancient magnets being made by rubbing iron on lodestones.
• It might be unsatisfying, but that's it. Permanent magnets are made of up smaller magnets called domains, and domains are made of magnetic atoms all pointing in the same direction. Those atoms are magnetic because of electrons (which are the tiniest magnets) agreeing to point in the same direction. Magnets are made of magnets.
• Most commonly we see iron magnets and neodymium magnets these days. 
• Here's the short of how special relativity leads to magnetic fields:

  • The faster something moves relative to observer, the less length it has (aka the shorter it is) according to observer.
• Here's the short of how special relativity leads to magnetic fields:

  • Because things moving results in them getting shorter- they get more compact.
  • This results in the charges flowing in a wire becoming closer together- resulting in a higher charge density.
  • The higher charge density causes an electric force to come in to effect via Coulomb's law within a moving observer's reference frame.
• Basically, magnetic fields are the force fields created by, and felt by, moving charges aka currents.