A very small .0009 kg mass carries a charge of -83.09 `microC and is located at the point ( .32 m,0,0). A charge of -45.06 `microC is located at the origin and fixed at that point. Find the x component of the acceleration of the mass, assuming that the only force present is the electrostatic force between the charges.
The charges are separated by .32 m. The magnitude of the force between the charges is therefore given by Coulomb's Law as
This force will act on the .0009 kg mass to which the charge is attached, giving it an acceleration of magnitude
Since the particles repel, this acceleration will be away from the origin; the x component of the acceleration will therefore be 365500 m/s^2
Coulomb's Law generalizes our observations of forces between charges into the statement F = k q1 q2 / r^2, where q1 and q2 are two charges and r the distance between them. If q1 is fixed at the origin and q2, of mass m, is located at (x,0,0), then we see that r = x so the magnitude of F is k q1 q2 / x^2. The acceleration of mass m attached to this charge is therefore a = F / m = k q1 q2 / (x^2 m).
The figure below shows how the distance r between charges is r = (x - 0) = x. The repulsive nature of the force is indicated by the direction of the force vector. The acceleration of the free charge q2 will be in the direction of the force vector.
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