A charge of -0.600 micro-Coulombs exerts an upward 0.160-Newton force on an unknown charge 0.350 meters directly below it.
What is the unknown charge (magnitude and sign)?
What is the magnitude of the force that the unknown charge exerts on the charge of magnitude -0.600 micro-Coulombs?© BrainMass Inc. brainmass.com December 24, 2021, 7:35 pm ad1c9bdddf
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First of all, the charges attract each other. Hence they have opposite signs.
Since the known charge (q1) is negative, the unknown charge (q2) must be positive.
The formula for the magnitude of the Coulomb force is
F = (k *q1 * q2) / (r^2),
where k is a constant: k=9x10^9 N(m^2)/(C^2)
q1 and q2 are the charges
r is the distance between the charges.
Thus solving for q2:
q2 = (F * r^2) / (k *q1)
Plugging in the numbers:
r = 0.35 m
q1 =0.6 micro-Coulombs = 0.6x10^(-6) C (note that we don't care here about the sign; we are interested in the magnitude only)
F = 0.16 N
And we get
q2 = [(0.16 N) * (0.35 m)^2] / [9x10^9N(m^2)/(C^2) * 0.6x10^(-6) C] = 3.6x10^(-6) C
q2 = 3.6 uC
so the unknown charge is 3.6 micro-Coulombs and is positive.
Newton's third law states that for every action there is an equal and opposite reaction.
Therefore, q2 applies the same magnitude of force on q1 as q1 applies on q2 (only in the opposite direction).
So the force q2 applies on q1 is 0.16 N
I hope this helps.
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