184_notes:mag_interaction

This week we are going to start to talk about a new kind of interaction: the magnetic interaction. Pieces of this section may feel familiar from when we talked about the electric interaction, while other pieces will feel new. As we will talk about in a couple of weeks, the electric field is related to the magnetic field, but for historical reasons, we often define them as separate interactions. Just as we did with the electric interaction, these notes will start with the basics of the magnetic interaction and introduce the idea of a magnetic field.

Rather than talking about the two types of charges (positive and negative), with magnets we talk about the two magnetic poles - north and south poles. Magnetic poles are not the same thing as electric charges, although they do interact in similar ways. (Again, this is because the magnetic interaction is related to the electric interaction as we will see later.) We observe that a north pole on a magnet will repel another north pole and a south pole will will repel other south pole - following the “likes repel” rule. Whereas, we observe that a north pole will attract a south pole of a magnet - following the “opposites attract” rule. However, unlike with electric charges, a single magnetic pole (sometimes referred to as “monopole”) does not appear to exist. For example, as far as we know, it is impossible to have a single north pole magnet - instead a magnet always comes with both a north and south pole. Even if you cut a magnet in half, each half will then have a north and south pole. While we believe these monopoles do not exist, some theoretical descriptions of the universe require them and physicists are actively scouring the universe for any sign of magnetic monopoles. We will talk about why we think magnetic monopoles do not exist later.

Also similar to the electric interaction, if you have stronger magnets or if the poles are closer together, there is a stronger magnetic interaction. You may have felt this if you have ever tried to push two repelling magnets really close together - the closer you bring them, the harder they push each other apart.

Again, these rules may seem simple or obvious, but they can be extremely powerful tools to help you check your work and to describe how magnets interact with one another. If your solution says you have only a north pole (without a south), or if you get answer that says the north pole is repelling a south pole, you know that you made a mistake somewhere in your solution.

We will be focusing on describing and understanding the magnetic field, which is a vector field that can be produced by a permanent magnet (like a fridge magnet), a single moving charge, or by an electric current (many moving charges). Since it is a vector field, this means that the magnetic field has both a magnitude and a direction.

As $m$ is already used for mass, we represent the magnetic field by a $\vec{B}$. Because we use B as the letter variable, you may see books (or instructors) shorten “magnetic field” to just a “B-field”. The SI units for magnetic field are given typically in “teslas” (named for Nikola Tesla) and abbreviated with a “T”. A 1 T field is a very large magnetic field. For comparison, the Earth's magnetic field is about $32*10^{-6}$ T, a refrigerator magnet has a magnetic field of about $0.005 T$, and a MRI (magnetic resonance imaging) machine has a magnetic field of $1-5$ T. As you can see in this video, a 4 T B-field is capable of producing huge amounts of force and can move large objects like chairs or oxygen tanks across the room. The largest (sustained) magnetic field that we have produced on Earth is about 45 T. Larger magnetic field exist in extraterrestrial situations such as stars, galaxies, and black holes. But, if you come across a situation with a magnetic field that is larger than about 45 T, it probably is not realistic or, at a minimum, it is not occurring on Earth.

Because a telsa is such a large magnetic field, you may sometimes come across a magnetic field given in units of “gauss” or “G” (named after Carl Gauss), where $1T=10,000G$. However, since teslas are the SI unit, we will be working with those.

The rest of the notes in this week will go into more detail about what the magnetic field looks like and how we can calculate the magnitude/direction for the various sources of magnetic fields.

• 184_notes/mag_interaction.txt