The electrostatic force between two charged objects is given by Coulomb's law:
F = k * (q1 * q2) / r^2
where F is the force, k is Coulomb's constant (9 x 10^9 N*m^2/C^2), q1 and q2 are the charges of the two objects, and r is the distance between them.
In this case, we have two balloons with charges of 8.37 µC and q2 (unknown), separated by a distance of 30 mm, and experiencing a repulsive force of 0.5 N.
We can plug in the given values and solve for q2:
0.5 N = (9 x 10^9 N*m^2/C^2) * (8.37 µC * q2) / (0.03 m)^2
Simplifying:
q2 = (0.5 N * 0.03 m^2) / (9 x 10^9 N*m^2/C^2 * 8.37 µC)
q2 = 2.05 µC
Therefore, the unknown charge is 2.05 µC.