If the distance between two charge particles is increased by four, the force will decrease by a factor of?

According to Coulomb's law, the magnitude of electrostatic force of attraction between two point charges is directly proportional to product of magnitudes of charges and inversely proportional to the square of the distance between them.

Mathematically,      F = \frac{q_{1}q_{2}}{r^{2}}

where         F = force

                q_{1} = charge 1

                q_{2} = charge 2

               r = distance between the charges

Therefore, when distance is increase by four times then the force will decrease by a factor of 16 as force is inversely proportional to the square of distance.

Explanation:

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C. A beetle that infects ash trees is introduced to the land

Explanation:

The Land's carrying capacity for ash trees can be said to be the maximum number of ash tree population that the tract of the conservation land can adequately cater for and support.

From the listed options given, the event that would have little effect or the least effect on the land's carrying capacity for ash trees is option C "A beetle that infects ash trees is introduced to the land", simple because the impact won't be as intense and direct just as the other events would be.

For example, if maple trees are introduced, there would be competition with the ash trees for the limited resources, thereby putting a pressure on the land. Also, draining of half of the water of the land caused by human activities would bring about a drop in the amount of water available for the survival of the ash trees. Lastly, the effect of deforestation as one third of the ash trees are cut down, would be huge and largely felt.