# 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.