Coulomb's Law and Simple Harmonic Motion

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SUMMARY

The discussion focuses on the application of Coulomb's Law to demonstrate that a third charge +q, when displaced from equilibrium between two fixed charges +Q, will execute simple harmonic motion (SHM). The force acting on charge +q is calculated using Coulomb's Law, yielding F = -4kQqs/d³. This force can be compared to Hooke's Law for springs, establishing a relationship that allows for the derivation of the oscillation period T. The conclusion is that the system behaves analogously to a spring-mass system, confirming the SHM characteristics.

PREREQUISITES
  • Coulomb's Law (F = kQ1Q2/r²)
  • Understanding of Simple Harmonic Motion (SHM)
  • Knowledge of Hooke's Law (F = -kx)
  • Basic calculus for deriving equations of motion
NEXT STEPS
  • Derive the oscillation period T for a mass-spring system
  • Explore the relationship between electric forces and mechanical forces in oscillatory systems
  • Study the conditions for SHM in different physical systems
  • Investigate the effects of varying charge magnitudes on oscillation characteristics
USEFUL FOR

Physics students, educators, and anyone interested in the principles of electrostatics and oscillatory motion, particularly in the context of Coulomb's Law and SHM.

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Homework Statement


Two positive charges +Q are affixed rigidly to the x-axis one at x = -d and the other at x = +d. A third charge +q of mass mwhich is constrained to move only in the x-axis is displaced from th eorigin by a small distance s << d and then released from rest. Show that q+ will execute simple harmonic motion and determine the oscillation period T.


Homework Equations


Coulomb's Law F=kQ1Q2/r2
*possibly something else to relate this to SHM*


The Attempt at a Solution


I found the force from coulomb's law, F= -4kQqs/d3
but i really don't know how to relate this to SHM so i can derive an equation for period.
 
Physics news on Phys.org
Compare your expression for the force with the force exerted by a spring in a mass. How is the spring force related to the displacement of the mass from the equilibrium position?
 

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