Biot-Savart: Calculates magnetic field from a small current segment, useful for complex geometries. | Ampère’s Law: Relates magnetic field around a closed loop to the enclosed current, useful for symmetrical situations.

Moving Charge: Force is on a single charge, F = q(v x B). | Current-Carrying Wire: Force is on the entire wire, F = ILBsinθ.

A vector field that exerts a force on moving electric charges, electric currents, and magnetic materials.

A fundamental source of magnetic fields, analogous to a tiny bar magnet with a north and south pole.

A measure of how much a material can be magnetized in response to an external magnetic field.

A constant that represents the baseline for how easily a magnetic field can form in a vacuum.

Materials (like iron, nickel, cobalt) that can be permanently magnetized due to aligned magnetic domains.

Materials (like aluminum, titanium, magnesium) weakly attracted to magnetic fields; dipoles align temporarily.

Materials (all materials) weakly repelled by magnetic fields due to slight alignment of electron dipole moments opposite to the external field.

Point your thumb in the direction of the velocity, your fingers in the direction of the magnetic field, and your palm will point in the direction of the force.

Point your thumb in the direction of the current, your fingers in the direction of the magnetic field, and your palm will point in the direction of the force on the wire.

1. Choose an Amperian loop. 2. Calculate the line integral of the magnetic field around the loop. 3. Determine the current enclosed by the loop. 4. Apply the formula: $\oint B \cdot dl = \mu_0 I_{enc}$.