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

`5.0\cdot 10^(-6)C`

Step-by-step explanation:

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

`F=k(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=(kq^2)/(r^2)\\q=\sqrt{(Fr^2)/(k)}=\sqrt{((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).