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= Textbook =
*[https://openstax.org/books/university-physics-volume-2/pages/11-introduction University Physics Volume 2: Chapter 11 - Magnetic Fields]

== Ferromagnets and Electromagnets ==
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Materials such as iron, cobalt, and nickel exhibit strong magnetic properties due to the alignment of their atomic magnetic moments. Ferromagnetic domains align to create a net magnetic field.

Electromagnets use electric current to generate a magnetic field. The magnetic field strength is proportional to the current and the number of coils.

The magnetic properties of materials arise from:
* The spin of electrons,
* The orbital motion of electrons around the nucleus.

== Application of Ferromagnets and Electromagnets ==
* MRI machines (Electromagnets),
* Hard drives (Ferromagnets),
* Electric motors (Electromagnets),

= Magnetic Field Lines =
Magnetic field lines represent the direction and strength of the magnetic field. 
* Magnetic field lines flow from the north pole to the south pole of a magnet.

= Motion of a Charged Particle in a Magnetic Field =

== Force on a Moving Charge ==
The force <math>\vec{F}</math> on a moving charge <math>q</math> in a magnetic field <math>\vec{B}</math> is given by the Lorentz force:
* Formula: <math>\vec{F} = q \cdot (\vec{v} \times \vec{B})</math>
  Where:
  * <math>\vec{v}</math> is the velocity of the charge,
  * <math>\times</math> denotes the cross product.

== Applications ==

=== Northern Lights ===
Charged particles from the solar wind are guided by the Earth's magnetic field, exciting atmospheric gases and producing visible light.

=== Van Allen Belt ===
Regions of trapped charged particles in the Earth's magnetic field. These particles spiral along magnetic field lines.

=== Mass Spectrometer ===
Used to measure the mass-to-charge ratio of ions. 
* Formula: <math>r = \frac{mv}{qB}</math>
  Where:
  * <math>r</math> is the radius of the ion's path,
  * <math>m</math> is the ion's mass,
  * <math>v</math> is the ion's velocity,
  * <math>q</math> is the charge,
  * <math>B</math> is the magnetic field strength.

=== Cyclotron ===
A type of particle accelerator that uses a perpendicular magnetic field to accelerate charged particles in a circular path.
* Formula: <math>r = \frac{mv}{qB}</math>

= Crossed Fields =

== Force on a Moving Charge due to Electric and Magnetic Fields ==
The force on a charge moving in both electric <math>\vec{E}</math> and magnetic <math>\vec{B}</math> fields is:
* Formula: <math>\vec{F} = q \cdot (\vec{E} + \vec{v} \times \vec{B})</math>

== Thomson Experiment (Discovery of the Electron) ==
Used crossed electric and magnetic fields to determine the charge-to-mass ratio of the electron.

== Hall Effect ==
The creation of a voltage difference across an electrical conductor, transverse to the electric current and the applied magnetic field.

= Magnetic Force on a Current-Carrying Wire =
The force on a wire of length <math>L</math> carrying current <math>I</math> in a magnetic field <math>B</math> is:
* Formula: <math>\vec{F} = I \cdot (\vec{L} \times \vec{B})</math>

= Torque on a Current Loop - the Electric Motor =
A current loop in a magnetic field experiences torque, which is the basis for electric motors.
* Formula: <math>\tau = n \cdot I \cdot A \cdot B \cdot \sin(\theta)</math>
  Where:
  * <math>\tau</math> is the torque,
  * <math>n</math> is the number of loops,
  * <math>I</math> is the current,
  * <math>A</math> is the area of the loop,
  * <math>B</math> is the magnetic field,
  * <math>\theta</math> is the angle between the magnetic field and the normal to the loop.


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= Simulations =
Understanding the earth's magnetic field:

* [http://phet.colorado.edu/en/simulation/magnet-and-compass Bar Magnet and compass]
* [http://www.windows2universe.org/physical_science/magnetism/earth_magnet_dipole_interactive.html Earth's magnetic Field]
* [https://www.youtube.com/watch?v=M9Gdm_OXKz4, demo of magnetic field lines with iron filings (one magnet)]<br>
* [https://www.youtube.com/watch?v=GCHJmMdHNPo, demo of magnetic field lines with iron filings (two magnets)]<br><br>

Vector Product:

* [http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/Vectors/CrossProduct/CrossProduct.swf Cross product of two vectors]
<!--* [http://www.phy.syr.edu/courses/java-suite/crosspro.html Cross product of two vectors-with expalnations]-->

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