# 5. Summary

- Permanent magnets have two ends, arbitrarily labeled
*north*and*south*based on how they align with the Earth's magnetic field. Magnetic monopoles do not exist; every magnet has a north*and*south pole. - The magnetic field, or \(\mathbf{B}\) field, is a vector field, and points in the direction a compass would point "north" if it were placed in the field.
- An electric charge feels a force in a magnetic field only if the charge is in motion. The magnitude of the force is given by \[| \mathbf{F} | = |q| |\mathbf{v}| |\mathbf{B}| |\sin \theta| = |q| |\mathbf{v}_{\perp}| |\mathbf{B}| \]The magnitude of the force depends on the magnitude of the velocity
*perpendicular to the field*. \(|\mathbf{v}_{\perp} |=|\mathbf{v}| |\sin \theta|\) where \(\theta\) is the angle between the field vector and velocity vector. - Moving charges also create magnetic fields. Permanent magnets give off \(\mathbf{B}\) fields because of the collective motion of the electrons within them.
- We learned the Right-Hand Rule for finding the direction of the force on a moving charge in a magnetic field. We learned the Right-Hand Rule for finding the direction of a magnetic field around a wire carrying current.
- One can induce a current in a circuit by changing the flux of the \(\mathbf{B}\) field through the area enclosed by the circuit. Faraday's law states that the induced EMF \(\mathcal{E}\) (voltage) is proportional to the change in flux over time: \[\mathcal{E} = -N \dfrac{\Delta \Phi}{\Delta t}\]Lenz's law states that induced currents flow in the direction that
*opposes*change in flux.