# A charge in motion

A particle of mass $$m$$ and charge $$q$$ is projected with $$\overrightarrow { v } ={ v }_{ 0 }\hat { i }$$ in a non uniform magnetic field which is given by $$\rightarrow \overrightarrow { B } =-{ B }_{ 0 }x\hat { k }$$ , where $${ B }_{ 0 }, { v }_{ 0 }$$ are positive constants. Find the maximum $$x$$ coordinate of the particle during its motion.

Details and Assumptions

Assume that the particle enters the $$x-y$$ plane at origin with the given velocity.

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