# Kinetic Energy of a Charged Particle

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?

Part II

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

-PLEASE EXPLAIN PROBLEM AND INCLUDE NUMERICAL SOLUTION AND + OR - IF NEEDED.

Â© BrainMass Inc. brainmass.com December 24, 2021, 8:36 pm ad1c9bdddfhttps://brainmass.com/physics/work/kinetic-energy-charged-particle-293114

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Hello and thank you for posting your question to Brainmass!

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

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.

Â© BrainMass Inc. brainmass.com December 24, 2021, 8:36 pm ad1c9bdddf>https://brainmass.com/physics/work/kinetic-energy-charged-particle-293114