Three charges, each of strength Q (Q > 0) form a fixed equilateral triangle with sides of length b. You throw a particle of mass m and positive charge q from far away, with an initial speed v. Your goal is to get the particle to go to the center of the triangle, your aim is perfect, and you are free to throw from any direction you like. What is the minimum possible value of v?

Physics for Scientists and Engineers: Foundations and Connections
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Author:Katz, Debora M.
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Chapter24: Electric Fields
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Problem 14PQ: A particle with charge q on the negative x axis and a second particle with charge 2q on the positive...
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Three charges, each of strength Q (Q > 0) form a fixed equilateral triangle with sides of length b. You throw a particle of mass m and positive charge q from far away, with an initial speed v. Your goal is to get the particle to go to the center of the triangle, your aim is perfect, and you are free to throw from any direction you like. What is the minimum possible value of v?

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For minimum speed, When particle just reach at desired position then its speed at that point becomes zero which its kinetic energy at that point also becomes zero.

So total energy of particle when it reached at centre of triangle will be only potential energy and when it was far away then it’s total energy was only kinetic energy.

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