Calculating Point Charge from Kinetic Energy and Electric Potential

AI Thread Summary
The discussion revolves around calculating the charge Q of a point charge located at the origin, based on the kinetic energy and electric potential of a particle released from rest. The particle, with a mass of 0.005 kg and a charge of 2 µC, experiences a kinetic energy of 0.28 J as it moves from x=3 m to x=0.5 m. The conservation of energy equation is applied, leading to the equation involving the Coulomb constant and the charges. An initial calculation yielded Q as approximately -9.34 x 10^-12 µC, but the participant realizes a mistake in their approach. The discussion highlights the importance of careful application of energy conservation principles in electrostatics.
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Homework Statement


A point charge Q resides at the origin. A particle of mass 0.005 kg carries a charge of 2 µC. The particle is released from rest at x=3 m. Its kinetic energy as it passes x=0.5 m is 0.28 J. The Coulomb constance is 8.99x10^9 N*m^2/C^2. Find the charge Q. Answer in units of µC.


Homework Equations


Conservation of energy: PE_f + KE_f = PE_i + KE_i


The Attempt at a Solution


KE_i = 0 (starts from rest)
PE_i = kqQ/xi = kqQ/3
KE_f = .28 j
PE_f = kqQ/.5
kqQ[(1/.5) - (1/3)] = - .28
(8.99 x 10^9)(2)Q[1.66667] = -.28
Q = -9.3437152 x 10^-12 µC

What am I missing or doing wrong?
 
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(8.99 x 10^9)(2)Q[1.66667] = -.28
Q = -9.3437152 x 10^-12 µC
The given charge is 2μC
 
Oh wow! Stupid mistake.
 
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