An electron is placed in an electric field and is allowed to accelerate for a distance of 1 m. If the strength of the electric field is E = 200 V/m then what is the final velocity of the electron, assuming it starts from rest?

Question

anonymous · Answer

OK. Well, in 1 meter, the electron moves through a potential difference of 200 V.
Now, 1 eV is the energy gained by an electron in moving through a potential difference of 1 volt. So
the electron gains 200 eV of energy.

1eV = 1.6 * 10^-19 Joules.
200 eV = 200 * 1.6 * 10^-19 J
so this must be the kinetic energy gained by the electron.

Kinetic energy = (1/2) m v^2
so

200 * 1.6 * 10^-19 = 9.11 * 10^-31 v^2 / 2

v^2 = (2 * 200 * 1.6 * 10^-19) / (9.11 * 10^-31)

v^2 = 70.25 * 10^12
v = √(70.25 * 10^12) 
v = 8.4 * 10^6 m/s