Magnetic Fields
E-Field and Potential Recap
Magnetism
Any time a charge moves it generates a magnetic field. Why this occurs is thankfully out of the scope of the MCAT. As it involves a thorough understanding of Einstein’s Theory of Relativity and a lot of math.
As we go through and explore magnetism in more detail try and recall how electric fields work. We are going to see an array of similarities between both and we will learn more about why magnetism arises at a subatomic level when we look into the electronic structure of atoms.
Magnetic Fields
Magnetic fields (B), like electric fields, are fields that surround magnetic materials and moving charges. The strength of these magnetic fields measured by the Telsa (T) or gauss depending on the size (1 T = 104 gauss) vary both in strength and what produced them as we will see later.
As with electric fields, magnetic fields are also depicted using field lines. Since we don’t have positive and negative magnets the lines will originate and point outwards from the North (+) pole of fixed magnets and point inwards towards the South (-) pole of fixed magnets like those of a bar magnet or the Earth.
Unmoving Magnets
Why is it that a stationary magnet produces a magnetic field, it isn’t moving after all? This is true at a macroscopic level but when we dive into the microscopic realm of subatomic particles not so. Many of these particles including electrons are spinning, orbiting, and zipping around. Since electrons carry a negative charge and are in motion they generate magnetic fields that account for the magnetic properties of most materials.
Not all materials are magnetic though. This occurs because even though the electrons in all materials are moving the magnetic fields they generate interfere with one another. In materials such as wood, glass, and plastic all of the magnetic fields generated by the movement of various electrons end up canceling out. We call these materials diamagnetic and they have paired up electrons.
In other materials, the magnetic fields don’t cancel and result in materials that produce magnetic fields even when they aren’t moving. We call these materials paramagnetic and ferromagnetic and they have unpaired electrons. The big difference between a paramagnetic and ferromagnetic material is what they do when placed under the influence of a magnetic field.
Both start with their atomic magnets pointing in random directions and when both are placed into a magnetic field they align their atomic magnets with the field. Their behavior diverges when taken out of this magnetic field, however. The paramagnetic material will revert back to its former random orientation and quickly lose its magnetic field. Ferromagnetic materials, however, retain their orientations and with it their magnetic fields. This is why ferromagnetic materials such as iron, cobalt and nickel are used to create bar magnets.
Moving Magnets and The Donut of Truth
If even a single moving electron can generate a magnetic field then so can a whole mass of moving charge. And the more charges we move at once the stronger the magnetic field. This means that surrounding wires, axons, the core of the Earth, and anywhere else charges are moving in a coordinated fashion we will see magnetic fields.
If we wish we can quantify this using several different equations, but before going into each let’s first learn how to predict the direction of a magnetic field. On the MCAT we are only concerned with predicting the magnetic fields generated by wire or other objects that are modeled as wires. To determine the direction of magnetic fields we will use the first of two right-hand rules.
In both rules, our thumb and fingers will stand for the same components even though they allow us to determine different phenomena. Our thumb will point in the direction of the current or moving charge and shooting out of our fingers is the magnetic field. When considering a wire we start by pointing our thumb in the direction of the current in the wire and then curl our fingers around the wire to determine the direction of the magnetic field.
Our curled fingers demonstrate the circular magnetic fields that surround current-carrying wires. These circular fields continue outwards concentrically getting further apart as we move away from the wire.
Xs and Os
3D representations of magnetic fields don’t translate too well to our 2D pieces of paper. So physicists decided to represent magnetic fields that come straight out of the page as little dark circles while fields pointing straight into the page are Xs. I always struggled to keep these straights so lets work through a way to do just that now!
To begin we will need to imagine these arrows like the ones used in archery. With a tip on one side and fletching on the other. When an arrow comes at us we will imagine that it pokes our eye out this would leave us with an eye patch or a dark circle for an eye. So a collection circles represents a magnetic field that points out of the page.
On the other hand, if an arrow was traveling away from us, we would see the fletching which is X-shaped, so Xs travel away from us and into the page. There fore a collection of Xs represent magnetic fields that point into the page.
Magnetic Flux
If we draw boxes and measure flux just as we did with electric fields we would see that the flux drops the further away we get from the wire. Thus the magnetic field drops in strength the further we get from the wire.
If we want to quantify the strength of the magnetic field (B) at any point we can use the following equation:
[latexpage]
\[B=\frac{\mu_0I}{2\pi r}\]
Here μ0 is a constant that defines the permeability of free space (4π x 10-7 Tm/A), basically how much cancellation of the magnetic field occurs, I is the current in the wire, and r is the perpendicular distance away from the wire.
MRI: Giant Loops of Wire
The above equation only works for a straight wire and the minute we change its shape the equation breaks down. On the MCAT it is unlikely that you will encounter weird shapes, such as Mickey mouse shaped wires, but there is one other situation we must know, a loop of wire.
In loops, the right-hand rule we already discussed holds however when we go around various points of the loop we will notice that our fingers always point towards the center of the circle. There the magnetic field shoots straight out or into the page. This fact is important because it is the only point where the magnetic field is quantifiable. Here the variables are the same with the exception of r which stands for the radius of the loop. This makes sense since this is the only distance that we can reliably predict.
[latexpage]
\[B=\frac{\mu_0I}{2r} \]
One way I have seen this idea come up consistently is in the context of an MRI. An MRI or magnetic resonance imaging device is at its simplest a giant loop of wire through which massive quantities of current are run. Allowing them to generate incredibly strong magnetic fields ranging from 0.5T to 3T. The generated field causes the hydrogen atoms in both water and fat to align with the field which then decay and emit radio waves that can be measured. Allowing us to accurately map with high-resolution water and fat-rich tissues. Sometimes they are colloquial termed donuts of truth due to their appearance and their ability to detect pathologies.
We don’t really need to understand the specifics of an MRI, but make sure you can determine the direction of a magnetic field generated by an MRI.
