Magnetism

Just like “positive” and “negative” charges, magnets have “north” and “south” poles. There is (at the time of writing 🤞) no such thing as a magnetic monopole: when you break a magnetic dipole in half, it becomes two new dipoles. This is very similar to electric stuff! Like charges repel, opposites attract. The only difference is that magnetic fields are often called “B” fields, which seems incredibly arbitrary to me… but what do I know?

Magnetic fields must be closed loops. This will be a question on the test! In fact, I wouldn’t be surprised 😉 if someone were to tell me that it was on at least one of the forms (versions) of the 2025 Magnetism test in a couple of different question formats…

Magnetic Materials
Ferromagnetic materials can be permanently magnetized by an external magnetic field (e.g. cobalt, iron, nickel). Paramagnetic materials are only magnetized temporarily (e.g. aluminum, titanium). If you don’t get it, you probably don’t need to anyways (remember: you only need a 70% or something to get a 5!). I haven’t seen a question that tests this in any of the FRQ or MCQ work I did.

Magnetic Permeability ()
The measurement of how magnetized a material becomes when exposed to an external electric field. Ferromagnetic materials have a high magnetic permeability. Permeability is NOT constant; it changes with factors such as temperature, orientation, and strength of the external magnetic field. Like electric permittivity, we have a constant magnetic permeability of free spaces, which equals New unit just spawned in! It’s called a tesla (these ones don’t explode in Las Vegas though).

Magnetic Field
An electric charge moving through a magnetic field can experience a magnetic force, that is equal to:

Biot-Savart Law (experimentally determined)

This somehow (??) shows that a current-carrying wire (or even a single charged particle) creates a magnetic field. Around every wire, there is a magnetic field around the wire (determined by the alternate right hand rule).

Ampère’s Law
Similar to Guass’s law:

Magnetic Field of a Solenoid
An ideal solenoid consists of a single, very long, current-carrying wire wrapped to form a hollow cylinder. In an ideal solenoid, the length of the wire is significantly greater than the diameter. Using Ampere’s Law, we can calculate the magnetic field through a solenoid (work omitted):

is the loop density, or the number of loops in the solenoid () divided by the total length () of the solenoid.

Magnetic Flux
Electric flux, but with magnetic field instead of electric field. The units are (unsurprisingly) which we (surprisingly) call webers, or

Gauss’s Law for Magnetism
If you loved Gauss’s Law, you will LOVE this. Gauss’s Law for Magnetism states that the magnetic flux through a Gaussian surface is equal to the closed surface integral which equals zero.

You’re gonna love this, too. We know that moving electric charges create magnetic fields… but apparently (remember that I don’t make the rules) moving magnetic poles create electric fields.

When a magnetic field changes over time, it can create the same effect as an electric potential difference, which is called an induced emf.

Faraday’s Law of Electromagnetic Induction

When a changing magnetic flux induces an emf, the force is NOT conservative.

Lenz’s Law
tells you the direction that a current will go when a change in magnetic flux induces an emf

Back EMF
Induced emf that decreases the current in an electric motor. Zero when the motor isn’t rotating, lower at slower rotation speeds. (You can use Lenz’s Law to determine why the change in magnetic flux induces the back emf).

Inductance
The inductance of a circuit element is its tendency to resist a change in current. Since a larger change in current will create more voltage pushback, the way I think of inductance is the measure of voltage pushback an inductor will generate as the current changes. Until now, we’ve assumed that changes in current are instantaneous. However, they actually aren’t (ugh, assumptions, am I right?) due to the tendency of some circuit elements to create a back EMF. The inductance is given by

Inductance of a Solenoid
As a consequence of the above equation (you can derive this with Ampere’s Law), the inductance of a solenoid is given by

Where

You can use Kirchhoff’s Loop Rule to determine that the power (i.e. the energy being stored in the magnetic field of the inductor) in a simple circuit (battery, resistor, inductor, switch) is equal to

At steady-state, inductors are basically “not there”.

MEMORIZE TIME CONSTANT EQUATIONS AND DERIVATION
WATCH or you’re cooked