Difficult# Inverse Square Dependence of Coulomb's Law

EANDM-LASKJC

At a distance $x$ away from the center point of a localized collection of charges you measure a force $F_1$ on a positive test charge $+Q$. The force points towards the localized collection. The maximum distance between the charges in the localized collection is less than $x$.

The test charge is now moved to a distance of $2x$ from the center of the the localized collection of charge and the force on the test charge is found to be $F_1 /10$. Doubling the distance again to $4x$ results in a further drop by a factor of 10 in the size of the force on the test charge.

Given these observations what can you conclude about the localized collection of charge?