Past exam of the mathematics course of the University of Cambridge / 2008 / ib / Paper 2 / 17B / iii / Solution

Newton's second law with the computed Lorentz force gives $m\dot{v}=-(B^2{\ell }^2/R)v$. Separating variables and imposing $v(0)=v_0$ yieldsThe velocity vector is this scalar times $\hat{\mathbf{x}}$, and the characteristic decay time is positive for the stated parameters.