A charge in motion

Electricity and Magnetism Level 3

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.

\sqrt { \frac { { v }_{ 0 }m }{ 2q{ B }_{ 0 } } }

\sqrt { \frac { {2 v }_{ 0 }m }{ q{ B }_{ 0 } } }

\sqrt { \frac { { v }_{ 0 }m }{ q{ B }_{ 0 } } }

2\sqrt { \frac { { v }_{ 0 }m }{ q{ B }_{ 0 } } }