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# 5. Summary

[ "article:topic", "authorname:ucd7" ]

1. 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.
2. 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.
3. 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.
4. Moving charges also create magnetic fields.  Permanent magnets give off $$\mathbf{B}$$ fields because of the collective motion of the electrons within them.
5. 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.
6. 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.