An infinitely long positively charged straight thread has a linear...

Electric field $\mathrm{E}$ at a distance $\mathrm{r}$ due to infinite long wire is $E=\frac{2 k \lambda}{r}$ Force of electron $\Rightarrow F=e E$$\begin{aligned} & F=e\left(\frac{2 k \lambda}{r}\right) \\ & F=\frac{2 k \lambda e}{r} \end{aligned}$$$<br />This force will provide required centripetal force$$\begin{aligned} \mathrm{F} & =\frac{\mathrm{m}^2}{\mathrm{r}}=\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{r}} \\ \mathrm{v} & =\sqrt{\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{m}}} \\ \mathrm{KE} & =\frac{1}{2} \mathrm{mv}^2=\frac{1}{2} \mathrm{~m}\left(\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{m}}\right) \\ & =\mathrm{k} \lambda \mathrm{e} \end{aligned}$$