How Is the Kinetic Energy of a Proton Calculated in an Electric Field?

[Peter G.]

Hi,

A proton initially at rest finds itself in a region of uniform electric field of magnitude 5.0 x 10⁶ Vm^-1. The electric field accelerates the proton for a distance of 1 km.

Find the kinetic energy of the proton.

So, what I did was the following:

KE = q * E * s

I then converted the result from J to MeV. I, however, get 5000 MeV and the book gets 500 MeV. Is my line of thought incorrect?

Thanks once again!

 

[vela]

Your answer is right for the given numbers.

 

[Peter G.]

Thanks! I checked and rechecked my calculations and numbers several times before posting here and I was about to go crazy! I guess the book made a mistake (everyone has the right to!)

 

[vela]

Given the numbers for the electric field and distance, you should be able to calculate the potential difference of 5000 MV between the two endpoints. Because the proton has charge e, to get the work done, you just stick an e in front of the V in the units. If you do that, you can see pretty easily 5000 MeV is correct. You don't need to worry that you made a mistake while converting units.