Final answer:
The force on the proton increases to 4 times its original value when an electron is moved from 1 meter away to 0.5 meters away, according to Coulomb's Law which states that the force is inversely proportional to the square of the distance. Option A is correct.
Step-by-step explanation:
When an electron and a proton are separated by a distance of 1 m, the force between them is governed by Coulomb's Law, which states that the electrostatic force (F) is proportional to the product of the two charges (q1 * q2) divided by the square of the distance (r) between them, and multiplied by a constant (k).
F = k * (q1 * q2) / r^2
When the electron is moved 0.5 m closer to the proton, the new distance between them becomes 0.5 m. According to Coulomb's Law, if the distance is halved, the force increases by a factor of four because it is inversely proportional to the square of the distance.
So, if the initial force is F, after the electron is moved closer to the proton, the new force will be:
New F = k * (q1 * q2) / (0.5 m)^2 = k * (q1 * q2) / (0.25 m^2) = 4 * (k * (q1 * q2) / (1 m)^2) = 4 * F
The correct answer to the question is:
A. It increases to 4 times its original value.