How would you change the distance between two charged particles to increase the electric force between them by a factor of 25? a. increase the distance by a factor of 5. b. reduce the distance by a factor of 5. c. reduce the distance by a factor of 25. d. increase the distance by a factor of 25.

Correct  
Option b: Reduce the distance by a factor of 5

The electric force between two charged particles is given by:



Here,

k is the Coulomb's constant
q and Q are the charges of two charged particles. 
r is the distance between them.

The formula shows that Electric Force is inversely proportional to the square of distance between charges. So if we want to increase the electric force we have to decrease the distance between them.

Moreover, electric force is inversely proportional to square of the distance. This means, the change in electric force will be the square of change in the distance between the charges. So, if distance is changed by a factor of 5, electric force will change by a factor of square of 5 which is 25.

Therefore, the correct answer to this questions is reduce the distance by a factor of 5 to increase the electric force between the charges by a factor of 25.