Change in Electric Force due to Distance Variation

In this physics problem, we need to find how the electric force between two charges changes when the distance between them is modified. Let's start by listing our given variables.

Initially, we have two charges, queue one and queue two, separated by a distance d. The resulting electric force is given as F.

According to Coulomb's Law, the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Now, let's look at the final state. The separation distance is changed to zero point eight seven times the original distance d.

Notice that the charges remain exactly the same. Only the distance changes. This allows us to use a ratio approach between the two forces.

We can write the relationship as the new force F sub two over the old force F sub one equals the inverse square of their distances.

Substituting our values, F sub one is F, the initial distance r sub one is d, and the final distance r sub two is zero point eight seven d.