A charge in motion

A particle of mass mm and charge qq is projected with v=v0i^\overrightarrow { v } ={ v }_{ 0 }\hat { i } in a non uniform magnetic field which is given by B=B0xk^\rightarrow \overrightarrow { B } =-{ B }_{ 0 }x\hat { k } , where B0,v0{ B }_{ 0 }, { v }_{ 0 } are positive constants. Find the maximum xx coordinate of the particle during its motion.

Details and Assumptions

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

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