Question

Consider an electron placed in a region of space in which the electric potential spatially. The electron is placed at a point where the potential is -1000V relative to ground, and it is observed to accelerate to a point where the potential is -500V relative to ground. How fast is the electron moving at that point, assuming nothing else impacts the electron's motion

Answer 1

Answer:

$1.33\cdot 10^7 m/s$

Explanation:

For a charged particle accelerated by an electric field, the kinetic energy gained by the particle is equal to the decrease in electric potential energy of the particle; therefore:

$K_f-K_i = -q\Delta V$

where

$K_f$ is the final kinetic energy

$K_i$ is the initial kinetic energy

q is the charge of the particle

$\Delta V$ is the potential difference

In this problem,

$q=-1.6\cdot 10^{-19}C$ is the charge of the electron

$\Delta V=-500 V-(-1000 V)=500 V$

The electron starts from rest, so its initial kinetic energy is

$K_i=0$

Therefore,

$K_f=-(-1.6\cdot 10^{-19})(500)=8\cdot 10^{-17}J$

We can write the final kinetic energy of the electron as

$K_f=\frac{1}{2}mv^2$

where

$m=9.11\cdot 10^{-31} kg$ is the electron mass

v is the final speed

And solving for v,

$v=\sqrt{\frac{2K_f}{m}}=\sqrt{\frac{2(8\cdot 10^{-17})}{9.11\cdot 10^{-31}}}=1.33\cdot 10^7 m/s$