Intuition and Magnetic Fields
Most recent answer: 10/17/2014
- 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.
(published on 10/17/2014)