Answer to Question #301972 in Electric Circuits for Diablo

Question

A proton with a speed of 2.0x10^5m/s enters a region of space in which source charges have created an electric field potential "v"; What is the proton speed after it move through a potential difference of 100volts.

- What will be the final speed if the proton replace an electron.

Mass of Proton = 1.67x10^-27kg

Mass of Electron = 9.1x10^-30kg

Answer 1

Given:

$v_i=2.0*10^5\:\rm m/s$

$V=100\:\rm V$

The energy-work theorem says

$$\frac{mv_2^2}{2}-\frac{mv_1^2}{2}=eV$$

$$v_2=\sqrt{v_1^2+2eV/m}$$

$$v_2=\sqrt{(2.0*10^5)^2+\frac{2*1.6*10^{-19}*100}{1.67*10^{-27}}}$$

$$v_2=2.43*10^5\:\rm m/s$$