Conservation of Energy and electric potential

[shorti2406]

The figure shows a graph of electric potential versus position along the x-axis. An proton is originally at point A, moving along in the positive x-direction. How much kinetic energy does the proton need to have at point A in order to be able to reach point E ( with no forces acting on the proton other than those due to the indicated potential)? How much kinetic energy does the electron need? Points B, C, and D have to be passed on the way.

I don't have a copy of the graph, but

A = 100 V
B = 0 V
C = -60 V
D = -20 V
E = 55 V


Okay so I know that since positive charges move through decreases in potential, and the potential and potential energy are greatest at A, the proton will spontaneously travel from point A to point E. So, Ka = 0.

But I'm really not sure how to calculate the kinetic energy for the electron. If someone could help me out, I'd appreciate it!

 

[Doc Al]

Okay so I know that since positive charges move through decreases in potential, and the potential and potential energy are greatest at A, the proton will spontaneously travel from point A to point E. So, Ka = 0.

OK.

But I'm really not sure how to calculate the kinetic energy for the electron.

Realize that the electron needs enough initial energy to get past each intermediate point. How much energy is needed to get to B? (Measure the KE in electron volts; once you get your final answer you can convert units if you wish.) Is that enough to take it to C? Etc. (Hint: To the electron, a negative potential difference represents a barrier. What's the steepest barrier (lowest potential) that the electron must overcome?)

 

[thepatientmental]

The kinetic energy of a charged particle can be calculated using the equation KE = qΔV, where q is the charge of the particle and ΔV is the change in potential energy between two points. In this case, the proton has a charge of +1 and the electron has a charge of -1, so their kinetic energies can be calculated as follows:

For the proton:
KE = (+1)(55 V - 100 V) = -45 J

For the electron:
KE = (-1)(55 V - 100 V) = +45 J

This means that the proton needs -45 J of kinetic energy at point A in order to reach point E, while the electron needs +45 J of kinetic energy. It is important to note that the signs of the kinetic energies are opposite for the proton and electron, as they have opposite charges and will therefore move in opposite directions along the potential gradient. Additionally, as the proton and electron move through points B, C, and D, their kinetic energies will change accordingly based on the changes in potential. Conservation of energy dictates that the total energy (potential + kinetic) of the particle will remain constant throughout its motion.