Aglass bead charged to 3.7nc exerts an 7.0×10−4n repulsive electric force on a plastic bead 2.9cm away. what is the charge on the plastic bead?

The charge on the plastic bead is 17.68 nC

Data obtained from the question Charge on glass bead (q₁) = 3.7 nC = 3.7×10¯⁹ CForce (F) = 7×10¯⁴ NDistance apart (r) = 2.9 cm = 2.9 / 100 = 0.029 mElectrical constant (K) = 9×10⁹ Nm²/C²Charge on plastic bead (q₂) =? How to determine the charge on the plastic bead

F = Kq₁q₂ / r²

7×10¯⁴ = (9×10⁹ × 3.7×10¯⁹ × q₂) / (0.029)²

Cross multiply

9×10⁹ × 3.7×10¯⁹ × q₂ = 7×10¯⁴ × (0.029)²

Divide both side by 9×10⁹ × 3.7×10¯⁹

q₂ = [7×10¯⁴ × (0.029)²] / (9×10⁹ × 3.7×10¯⁹)

q₂ = 17.68×10¯⁹ C

q₂ = 17.68 nC

Learn more about force on charges:

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The electrostatic force between the glass bead and the plastic bead is given by:

where
k is the Coulomb's constant
q1 is the charge of the glass bead
q2 is the charge of the plastic bead
r is the separation between the two beads

In this problem,  and , and since we know the force, , we can rearrange the equation to find q2, the charge of the plastic bead:

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