19) We are asked to consider the affect of distance on the electrostatic force between two objects. This question requires knowledge on Coulomb's Law of Electrostatic Force, which can be represented by the following red formula. The orange formula includes our given values for the electrostatic force.
Next, the problem asks what will happen to the force in the orange equation if we half the distance. Let's first take a look at the right side of the equation.
We can see that the equation is multiplied by 4 on the right side. In order to keep the equation equivalent, both sides must be multiplied by the same factor.
Thus, the force will be multiplied by a factor of 4. The force increases because it is multiplied by a factor greater than 1. If the force was multiplied by a factor between 0 and 1, for example 1/4, the force would decrease. So our final answer is that the force will increase by a factor of 4.
Answer: E
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