Intuition and Magnetic Fields

A moving object creates other phenomena in the direction of motion. For example, it may push things along its motion, or split things symmetrical about the direction of its motion. On the other hand, phenomena perpendicular to the direction of motion are counter-intuitive; we do not expect a blowing wind roll the objects perpendicular to the direction of wind—at least not in our universe. However, this is exactly what happens in another venue: A moving charge creates a perpendicular magnetic field! What is the explanation of perpendicularity? Why does not a moving charge create a magnetic field along the motion of charge—which would be more intuitive? Now, you may answer, that the universe does not act according to our intuition; OK. In fact an attribute of a good observer is to record exactly what he observes. However, after observation and data collection, a philosopher-physicist has to make sense of the phenomena; a mere relational explanation (mathematical or otherwise) does not satisfy his curiosity. The lingering “Why” has to be satisfied by an intuitive “Because”.
- Mehran (age 64)

I'm not sure we're obliged to convert mathematical facts to fit our intuition rather than gradually convert our intuition to fit the facts. But here's a try.

For the intuitive purposes you're discussing, a magnetic field is an intermediate step on the way to calculating the magnetic part of the force between two moving charged particles. Your intuition says that the physically important vector should be parallel to the motion, or maybe along the direction from the particle to the place where the effect is found, or maybe some combination of those directions. That leaves a plane of possible directions consistent with your intuition. Now the magnetic acceleration of the other moving particle is given mathematically by the cross product of it's velocity and the magnetic field, times some constants. That cross product is always at right angles to the field, so it's  always in exactly the plane that your intuition demands!

So think of the magnetic field as representing the direction along which the force cannot occur. 

Mike W.

(published on 10/17/2014)