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← 08ps-04 Parallel Plates Timing Solution

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Showing Revision 1 created 10/27/2012 by Amara Bot.

  1. The first thing I want to do when I solve this problem
  2. is to solve for the acceleration of the proton in this electric field.
  3. We know that the force on the proton is equal to the strength
  4. of the electric field E times its charge q.
  5. And we also know that the force is equal to the mass times acceleration.
  6. We get this equation here.
  7. And solving for a, I get that the acceleration is equal to
  8. the electric field strength times the charge of the proton over the proton's mass--awesome.
  9. Now that I have the acceleration, this problem just becomes a kinematics problem.
  10. I chose to use this kinematics equation here and we know that the proton
  11. has no initial velocity so this term drops out, and now I just want to solve for the time here.
  12. And doing some algebra here, I find that the time it takes for the proton to move
  13. from here to here is equal to the square root of 2 times the separation
  14. between the plates d over the acceleration a.
  15. And I know what the acceleration is. We just found it up here.
  16. Plugging in that value for acceleration, I get this equation for the time here.
  17. And putting in my numbers, I find that the time it takes for the proton to move
  18. from left to the right side of the plate is equal to 4.57x10⁻⁷ seconds,
  19. which is equal to 457 ns--good work.