Proton Deflection when traversing a a Parallel-plate Capacitor

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SUMMARY

The discussion focuses on calculating the sideways deflection of a proton as it traverses a parallel-plate capacitor with dimensions of 4.0 cm × 4.0 cm and surface charge densities of ±1.0×10−6C/m2. The proton, traveling at a velocity of 2.0×106 m/s, experiences a uniform electric field within the capacitor. The kinetic energy of the proton is calculated using the equation Ek=(1/2)mv2, resulting in Ek=1.67×10−21 J. The recommended approach to solve for the deflection involves using kinematic equations and Coulomb's Law to determine the acceleration and subsequent displacement.

PREREQUISITES
  • Understanding of electric fields and Coulomb's Law
  • Familiarity with kinematic equations in physics
  • Basic knowledge of kinetic energy calculations
  • Concept of uniform electric fields in parallel-plate capacitors
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  • Learn how to derive acceleration from electric fields in charged particle motion
  • Explore kinematic equations for projectile motion in physics
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Students studying electromagnetism, physics educators, and anyone preparing for exams involving electric fields and particle motion in capacitors.

Colton1995
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Homework Statement


A parallel-plate capacitor has 4.0cm × 4.0cm electrodes with surface charge densities ±1.0×10^−6C/m2. A proton traveling parallel to the electrodes at 2.0×10^6m/s enters the center of the gap between them.
Part A
By what distance has the proton been deflected sideways when it reaches the far edge of the capacitor? Assume the field is uniform inside the capacitor and zero outside the capacitor.


Homework Equations


Ek=(1/2)mv^2


The Attempt at a Solution


I solved for the kinetic energy using the above equation, Ek=(1/2)(1.67x10^-27kg)(2.0x10^6m/s = 1.67x10^-21J.
I'm pretty sure that I'm suppose to split it up into x and y variables to solve for delta y, but I am completely stuck. I would normally look at the answer and try to work it out from there but I am doing extra practice questions for review for my final and my prof. hasn't posted the answers yet. I'm not looking for an answer, but rather a push in the right direction. Thanks!
 
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I don't think using energy is the way to solve this problem. I would suggest just a simple kinematic approach using Coulomb's Law.
 
By using acceleration formula with electric field.
a= (P x E) / m
 

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