# Charged Particle In A Spatially Varying Magnetic Field

**Electricity and Magnetism**Level 4

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:**

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