The nature of magnetic interactions
Electric forces and potentials were similar in nature to the gravitational force studied in Physics 231. Magnetic forces seem completely different. Electric forces between two objects depended only on the charges of the two objects and their separation. Magnetic forces will also depend on the velocities of the two objects. Only moving charges create magnetic fields, and a charged object in a magnetic field must be moving in order to feel a force. For instance, the force experienced by two refrigerator magnets is due to the fact that the electrons in the material's atoms are rotating together.
The understanding of how movement factors into the equations for fields and forces makes magnetism one of the most difficult but interesting subjects in physics. It immediately brings up the question of frame dependence, "How can a force depend on the velocity, when an object's velocity depends on the velocity of the observer?". We will find that magnetic forces are much more than just an intellectual curiosity. Magnetic forces are essential for the operation of all electric motors. In fact they should more appropriately be called "magnetic motors". Magnetic forces are also used to guide and focus charged particles such as the electron beam in a computer's CRT display.