I know I have asked variations of this question in the past, but I am still
working on this one...
A region of space is filled with a uniform magnetic field, directed in the
z-direction, increasing linearly with time, with the "center of the field
at the origin. A small positively charged object located at the point (1
m, 0, 0) is released from rest.
I am trying to understand the resulting motion of the particle. Is any of
what I have so far correct:
At any point, it experiences a force caused by the induced electric field
associated with the changing magnetic field. That force is tangential to
the circle of radius r, where r represents the distance from the current
position to the center of the field. I think I can show that the field =
r/2 times dB/dt. That force increases the speed of the particle.
At any point, it also experiences the magnetic force that acts on any
particle moving perpendicularly through a magnetic field. But this field
happens to be increasing. This force changes the direction of the
particle's motion.
I am having trouble visualizing the resulting motion that these two forces
lead to.. Can anyone point me to a discussion of this topic? I am also
going to try to model this in interactive physics to see if I can get a
hint that way. Also, are there practical applications?