A charged particle is moving away from a uniformly charged infinite wire along a direction perpendicular to it. Initially, the particle is at a distance \(L\) from the wire moving with a velocity \(u\). When it is at a distance \(2L\), its velocity is found to be \(2u\). What will be the velocity of the particle when it is at a distance \(4L\) from the wire ?

Hint: Assume the uniform charge density of the infinitely long wire to be \(\lambda\) and the charge on the charged particle to be \(q\).

**Source:** IISER model question paper

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