Kinetic Energy of a Charged Particle

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Part 1

An electron starting from rest acquires 3.19 keV of kinetic energy in moving from point A to point B. How much kinetic energy would a proton acquire, starting from rest at B and moving to point A?
The kinetic energy is equal to the work done moving charge in the presence of a potential.
Thus, the electron's kinetic energy is:
(1.1)
Where is the charge of the electron and VAB is the potential difference between A and B.
And the kinetic energy of the proton:
(1.2)
Where is the charge of the electron and VBA is the potential difference between B and A.
But we know that the potential from A to B is negative the potential from B to A.
In addition , therefore:
(1.3)
Hence the kinetic energies of the electron and proton are the same.

Part II

Determine the ratio of their speeds at the end of their respective trajectories.

The kinetic energy for a particle of mass M and speed v is:
(1.4)
Therefore, according to (1.3) we get:

(1.5)
The mass of the proton is about 1840 time larger than the mass of the electron, hence:

The speed of the proton will be about 2.3% of the electron's speed.

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