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Question

A point charge +q & mass 100gm experiences a force of 100N at a point at a distance 20cm from a long infinite uniformly charged wire. If it is released its speed is 20lnxm/s when it is at a distance 40cm from wire. Find x.

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Solution

For the inifinite uniform charged wire, E=λ/2πϵor
at r=20cm, Force F=λq/2πϵo×0.2=100N
acceleration, a=λq/2πϵo×0.1=vdv/dr

so, v2/2=λ2πϵo×0.10.40.2lnr=200ln2

v=20ln2
Thus, x=2

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