Question 02/03
REFERENCE FRAMES
A positively charged particle starts moving with velocity V0
parallel to a uniformly positively charged infinite plate. The plate generates
field E perpendicular to it. The motion of the particle can be
described by a parabola; after a while it will acquire velocity V1
in the vertical direction and will continue to move with velocity V0
in the horizontal direction, as depicted in Fig. (a)
Now let us look at this motion in the reference frame moving with velocity
V0 to the right. As depicted in Fig. (b), the particle moves
with increasing velocity in the vertical direction, but does not move in the
horizontal direction. However, in this reference frame, the infinite plate moves to the
left with constant velocity and generates a magnetic field of size V0E/c
in the direction perpendicular to the plane of the picture. As a result, there is a force
acting on the particle in the horizontal direction, and consequently it must
accelerate!
Find the error in the above reasoning, and explain the apparent paradox.
This problem has been suggested by Lev Vaidman.
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