# Where does the particle stop?

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.

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