Charged Particle In A Spatially Varying Magnetic Field

A spatially varying magnetic field is given by B=B0xz^. B=-B_0 x \hat { z }. A particle of charge q q and mass m m leaves the origin with initial velocity v0 v_{0} in the positive x^\hat{x} direction. Find the value of xmaxx_\textrm{max}, the farthest horizontal displacement reached by the particle.

Details and Assumptions:

  • m=1 kgm = \SI{1}{\kilo\gram}
  • q=1 Cq = \SI{1}{\coulomb}
  • B0=1 T/mB_0 =\SI[per-mode=symbol]{1}{\tesla\per\meter}
  • v0=2 m/sv_0 = \SI[per-mode=symbol]{2}{\meter\per\second}

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