Mark creates a graphic organizer to review his notes about electrical force. which labels belong in the regions marked x and y?

a. x: decreasing to half will quadruple force y: doubling will double force
b. x: doubling will cut force in half y: decreasing to half will cut force in half
c. x: doubling will double force y: decreasing to half will quadruple force
d. x: decreasing to half will double force y: doubling will cut force in half

The correct answer is A

Explanation:

The question requires as well the attached image, so please see that below.

Coulomb's Law.

The electrical force can be understood by remembering Coulomb's Law, that  describes the electrostatic force between two charged particles. If the particles have charges and , are separated by a distance r and are at rest relative to each other, then its electrostatic force magnitude on particle 1 due particle 2 is given by:

Thus if we decrease the distance by half we have

So we get

Replacing we get

We can then multiply both numerator and denominator by 4 to get

So we have

Thus if we decrease the distance by half we get four times the force.

Then we can replace the second condition

So we get

which give us

Thus doubling one of the charges doubles the force.

So the answer is A.

X: Decreasing to half will quadruple force

Y: Doubling will double force