# Charged Particle In A Spatially Varying Magnetic Field

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

Details and Assumptions:

• $$m = \SI{1}{\kilo\gram}$$
• $$q = \SI{1}{\coulomb}$$
• $$B_0 =\SI[per-mode=symbol]{1}{\tesla\per\meter}$$
• $$v_0 = \SI[per-mode=symbol]{2}{\meter\per\second}$$
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