The center-to-center separation between two small charged spheres is doubled, the electric force between them?

Question

When the center-to-center separation between two small charged spheres is doubled, the electric force between is?

Answer 1

Coulombs Law:
F = k_e * Q * q / r^2

So when the distance between the spheres (r) is doubled, the r^2 term increased by a factor of 4. Since the r^2 term is in the numerator, the overall force decreases to 1/4 its original value.

Test it out, plug in some arbitrary values for r and watch what happens to the force.

For example,
lets say that k_e, q, and Q, all equal 1 (just for this example),
F = 1 / r^2
The only variable to change is r.
If we say that r = 1, then the force is,
F = 1 / 1^2 = 1 / 1 = 1
The lets double r, so now r = 2, so now the force equals,
F = 1 / 2^2 = 1 / 4 = .25
The force is now 1/4 of its initial value since r was doubled..

Answer 2

divided by 4