Question

Objects 1 and 2 attract each other with an electrostatic force of 18 units. If the charge of Object 2 is increased by a factor of 3 AND the distance separating Objects 1 and 2 is increased by a factor of 3, then the new electrostatic force will be _____ units.

Answer 1

`F'=18/3=6\ units`

Step-by-step explanation:

Electrostatic Force

We know particles 1 and 2 attract each other with an electrostatic force of 18 units. The force between two charged particles is given by Coulomb's formula

`\displaystyle F=(k\ q_1\ q_2)/(r^2)`

Where
`q_1,\ q_2` are the charges and r is the distance between them.

We are told the new charge 2 is

`q_2'=3q_2`

And the distance is three times the original

`d'=3d`

The new force is

`\displaystyle F'=(k\ q_1\ (3q_2))/((3r)^2)`

Operating

`\displaystyle F'=(3k\ q_1\ q_2)/(9r^2)`

`\displaystyle F'=(k\ q_1\ q_2)/(3r^2)`

This force is one third of the other one, so

`\boxed{F'=18/3=6\ units}`