# A particle spiraling in a magnetic field

Electricity and Magnetism Level 5

A particle with specific charge $$\alpha:= \frac{q}{m}=10^{8} \textrm{ C/kg}$$ enters a bubble chamber where its path can be observed. A magnetic field of induction $$B=10^{-2} \textrm{T}$$ is perpendicular to the particle's velocity. The particle experiences a viscous drag force which is approximately proportional to its velocity, that is $\vec{F}_{drag}=- k \vec{v}.$ As a consequence of this force, the particle spirals inward. It is observed that after two full rotations the radius of curvature decreases by $$2 \%$$. Then the magnetic field is switched off and the particle travels $$L=30 \textrm{cm}$$ before coming to a stop. What was the particle's velocity in m/s right before entering the chamber?

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