Question

An infinitely long line of charge has a linear charge density of 8.00×10^−12C/m.A proton is at distance 19.0cm from the line and is moving directly toward the line

with speed 1200m/s.How close does the proton get to the line of charge?

Answer 1

$$V_i-V_f=\frac{\lambda}{2\pi \epsilon_0}\ln {\frac{r_f}{r_i}}\\V_f-V_i=\frac{K_i}{e}=\frac{mv^2}{2e}$$

$$-\frac{\lambda}{2\pi \epsilon_0}\ln {\frac{r_f}{r_i}}=\frac{mv^2}{2e}\\ -\frac{8\cdot10^{-12}}{2\pi (8.85\cdot10^{-12})}\ln {\frac{r_f}{19}}=\frac{1200^2}{2(9.57\cdot10^{7})}\\r_f=18.0\ cm$$