Answer:
[tex]5.0\cdot 10^{-6}C[/tex]
Explanation:
The magnitude of the electrostatic force between two charged objects is given by Coulomb's law:
[tex]F=k\frac{q_1 q_2}{r^2}[/tex]
where:
[tex]k=8.99\cdot 10^9 Nm^{-2}C^{-2}[/tex] is the Coulomb's constant
[tex]q_1, q_2[/tex] are the two charges on the two objects
r is the separation between the two charges
The force is:
- Repulsive if the two charges have same sign
- Attractive if the two charges have opposite sign
In this problem:
F = 2.5 N is the force between the two balloons
r = 0.30 m is their separation
[tex]q_1=q_2=q[/tex] is the charge on each balloon (they have the same charge)
So, re-arranging the equation, we can find the value of q:
[tex]F=\frac{kq^2}{r^2}\\q=\sqrt{\frac{Fr^2}{k}}=\sqrt{\frac{(2.5)(0.30)^2}{8.99\cdot 10^9}}=5.0\cdot 10^{-6}C[/tex]
We are also told that the force between them is repulsive: this means that the charges on the two balloons have same sign (so, either they are both positive, or both negative).
