Question

Two spherical inflated rubber balloons each have the same amount of charge spread uniformly on their surfaces. If the repelling force is 2.5 N and the distance between the balloon centers is 0.30 m, find how much charge is on each balloon.

Answer 1

Answer:

$5.0\cdot 10^{-6}C$

Explanation:

The magnitude of the electrostatic force between two charged objects is given by Coulomb's law:

$F=k\frac{q_1 q_2}{r^2}$

where:

$k=8.99\cdot 10^9 Nm^{-2}C^{-2}$ is the Coulomb's constant

$q_1, q_2$ 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

$q_1=q_2=q$ is the charge on each balloon (they have the same charge)

So, re-arranging the equation, we can find the value of q:

$F=\frac{kq^2}{r^2}\\q=\sqrt{\frac{Fr^2}{k}}=\sqrt{\frac{(2.5)(0.30)^2}{8.99\cdot 10^9}}=5.0\cdot 10^{-6}C$

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).