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 $20\sqrt{lnx}m/s$ when it is at a distance $40cm$ from wire. Find $x$.

Answer 1

For the inifinite uniform charged wire, $E=\lambda /2\pi {ϵ}_{o}r$

at $r=20cm$, Force $F=\lambda q/2\pi {ϵ}_o\times 0.2=100N$

acceleration, $a=\lambda q/2\pi {ϵ}_o\times 0.1=vdv/dr$

so, $v^2/2=\frac{\lambda }{2\pi {ϵ}_o\times 0.1}{\int }_{0.2}^{0.4}lnr=200ln2$

$\Rightarrow v=20\sqrt{ln2}$

Thus, $x=2$