Kinetic Energy of Charged Particle

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SUMMARY

The kinetic energy of charged particle B, with mass m and charge 5Q, is determined using the principles of conservation of energy. Given that the initial potential energy (Ui) is 49.0683 J and the final potential energy (Uf) is 16.3299 J, the total kinetic energy (K) of the system is calculated as K = Ui - Uf, resulting in 32.7384 J. Since particle B has a charge of 5Q, its kinetic energy is half of the total system kinetic energy, yielding a final value of 16.3692 J for particle B.

PREREQUISITES
  • Understanding of electrostatic potential energy, specifically the formula U=kq1q2/r.
  • Familiarity with kinetic energy calculations using K=(mv^2)/2.
  • Knowledge of the conservation of energy principle, ΔU + ΔK = 0.
  • Basic grasp of Newton's laws of motion, particularly F=ma.
NEXT STEPS
  • Study the derivation and application of the electrostatic potential energy formula U=kq1q2/r.
  • Explore the concept of conservation of energy in mechanical systems.
  • Learn how to calculate the kinetic energy of a system of particles with varying masses and charges.
  • Investigate the implications of Newton's laws in multi-particle systems and their interactions.
USEFUL FOR

Students in physics, particularly those studying electromagnetism and mechanics, as well as educators seeking to explain the concepts of kinetic energy and potential energy in charged particle systems.

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[SOLVED] Kinetic Energy of Charged Particle

Homework Statement


Particles A (of mass m and charge Q) and B (of m and charge 5Q) are released from rest with the distance between them equal to 0.9976 m. If Q=33e-6 C, what is the kinetic energy of particle B at the instant when the particles are 2.9976 m apart?


Homework Equations


U=kq1q2/r
K=(mv^2)/2
ΔU+ΔK=0
F=ma

The Attempt at a Solution


I solved for the potential energy at both distances using U=kq1q2/r to find Ui=49.0683 J and Uf=16.3299 J. Then I used conservation of energy to find K so K=Ui-Uf and got K to be 32.7384 J. But I'm not sure how to get just the kinetic energy of particle B. I tried to sum the forces and use Newton's third law to find acceleration to see if that would help but I don't know how to find it without knowing the mass. I'm not sure if maybe I have to do a ratio to find the energy? I don't know what to do.
 
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nevermind, i figured out its just half of the system kinetic energy
 

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