Question

Two charged particles repel each other with a force F. If the charge of both particles is tripled and the distance between them is also tripled, then the force will be

Answer 1

The force will not change

Step-by-step explanation:

The electrostatic force between two charges is given by Coulomb's law:

`F=k(q_1q_2)/(r^2)`

where

k is the Coulomb's constant

q1, q2 are the two charges

r is their separation

In this problem:

- Each charge is tripled in magnitude, so

`q_1' = 3q_1\\q_2' = 3q_2`

- The distance is also tripled:

`r'=3 r`

Substituting into the original equation, the new force will be

`F' = k (q_1' q_2')/(r'^2)=k((3q_1)(3q_2))/((3r)^2)=k(q_1q_2)/(r^2)`

So, the force has not changed.