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 20√lnxm/s when it is at a distance 40cm from wire. Find x.
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×0.1∫0.40.2lnr=200ln2
⇒v=20√ln2
Thus, x=2