Coulomb's Law and insulating fiber

AI Thread Summary
Coulomb's Law is applied to a scenario involving a fixed charge and a bead that floats due to the balance of electric and gravitational forces. The charge Qa is -3 µC, and the bead's mass is 170 g, with its equilibrium position at 16 cm above the origin. The discussion reveals an error in unit conversion, as the charge should be expressed in Coulombs rather than microCoulombs. The calculations show that the Coulomb force must equal the gravitational force for equilibrium, leading to a derived charge Qb of approximately 1.58 nC. Clarification on unit consistency and signs is crucial for accurate problem-solving in electrostatics.
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A rigid, insulating fiber runs along a portion of the y-axis; the fiber isnot free to move. Gravity acts downward (g = 9.81 m/s2).A charge Qa = -3 µC is fixed to the fiber at the origin. A bead with a hole drilled through its center is slipped over the fiber andis free to move along the fiber without friction. The mass of the bead is m = 170 gand its charge is Qb. At equilibrium, the bead floats a distanceyb = 16 cm above the origin.
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the coulomb force must balance the gravitational force, so..
the answer is in C, not µC, so Q(a) = 0.003 C.
K * 0.003* Q(b) / 0.16^2 = 9.81 * 0.17
solving for Q(b), i get 1.581226667e-9.
i checked my solution, and it did equal to the gravitational force.
what am i doing wrong?
am i miscomprehending the problem, or the coulomb's law?
 
Last edited:
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check your units and signs,

0.003C \neq -3 \mu C

(there are two things that need to be changed to make this an equallity)
 
Last edited:
doh!
thanks. hehe.
 
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