Need help - about Coulomb's Law and SHM

AI Thread Summary
The discussion focuses on demonstrating that a negatively charged particle placed between two fixed positive charges exhibits simple harmonic motion (SHM) when displaced. The net force acting on the particle is derived using Coulomb's Law, resulting in a force equation that relates to acceleration. To confirm SHM, the relationship a = -ω²y must be established, requiring a recalculation of the total net force. The conversation emphasizes the importance of accurately calculating forces to derive the motion characteristics. This analysis connects Coulomb's Law with the principles of SHM.
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need help -- about Coulomb's Law and SHM

Two positive charges +Q are held fixed a distance d apart.
A particle of negative chage -q and mass m is placed midway between them, then is given a small displacement perpendicular to the line joining them and released. Show that the particle describes simple harmonic motion and find the period.
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i've found that the net force acting on the -q is
F = - (qQd) / [4(pai)(z)(y^2 + (0.5d)^2)]^(3/2) = ma
where z is the permittivity, and y is the displacement of -q

how i can show that a = - w^2 y?
 
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Well, you need to redo the calculation of the total net force.

Daniel.
 
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