Electric Potential Energy of A System of Point Charges

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SUMMARY

The discussion centers on calculating the kinetic energy of a particle with charge q = 7.5x10^-6 Coulombs, released from rest at 0.6m on the x-axis, influenced by a fixed charge Q = -20x10^-6 C at the origin. The user applied the conservation of energy principle, KE1 + U1 = KE2 + U2, but arrived at an incorrect kinetic energy of 9 Joules instead of the expected 4.5 Joules. The error was identified as a misunderstanding of the signs of potential energy in the context of attraction versus repulsion, emphasizing the need for consistent sign usage in calculations.

PREREQUISITES
  • Understanding of electric potential energy and kinetic energy concepts
  • Familiarity with Coulomb's law and the constant k = 8.99x10^9 N m²/C²
  • Knowledge of conservation of energy principles in electrostatics
  • Ability to perform calculations involving point charges
NEXT STEPS
  • Review the principles of electric potential energy in systems of point charges
  • Learn about the implications of charge signs in electrostatic interactions
  • Study the conservation of energy in electrostatic systems
  • Practice problems involving kinetic energy calculations for charged particles
USEFUL FOR

Students and educators in physics, particularly those focusing on electrostatics, as well as anyone involved in solving problems related to electric potential energy and kinetic energy in charged particle systems.

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A Particle of charge q=7.5x10^-6 Coulombs is released from rest at .6m on the x axis. The particle moves due to charge Q = -20x10-6 C. What is the Kinetic Energy of the particle the instant it has moved .4 meters if Q stays fixed at the origin?

Here I used KE1 + U1 = KE2 + U2
Which equals 0 + (kqQ)/.6 = KE2 + kqQ/.2
I got 2.2475 = KE2 - 6.7425
so KE2 = 8.99 or 9 Joules.
The answer is 4.5 J in the book however.

Where did I go wrong? My answer for the first part of the question, with Q =positive 20 micro Coulombs, was correct. Is the KE for attraction supposed to be multiplied by 1/2 as opposed to repulsion? Please help!

My k value by the way is correct, at 8.99x10^9.
 
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both potential energies should have the same sign. In your equation, one of them is positive the other is negative.
 

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