A charged particle enters a region where it experiences a drag force proportional to its velocity, that is, \[ \vec{F}_{drag}=- k \vec{v}. \] The initial velocity of the particle is \(v_{0}\). Because of this force, the particle stops and the magnitude of its displacement is \(L_{0}=10 \textrm{cm}\). The same experiment is repeated, this time a magnetic field \(B\) (perpendicular to the particle's velocity) is applied. The particle spirals and comes to a stop. Now the the magnitude of its displacement is \( L_{1}=6 \textrm{cm}\). What would be the particle's displacement \(L_{2}\) in meters if the magnetic field is reduced by a factor of 2? Note that in all three cases, the initial velocity of the particle is the same. Hint: This problem can be solved without calculus.
by
David Mattingly
