Two electrically-charges spheres are suspended from insulated threads a certain distance from each other. There is a certain amount of electrostatic force between them. Describe specifically (not just increase or decrease) what happens to this force in each of the scenarios below (1 pt. ea.):

a. The charge on one sphere is reduced by half
b. The charge on both spheres is doubled
c. The distance between the spheres is increased by a factor of three
d. The distance between the sphere is decreased to one-fourth
e. The charge of each sphere is doubled and the distance between them is doubled

k Q1Q2/d^2

plug and chug

Thank you, Sir Damon

To find the changes in the electrostatic force in each scenario, we need to understand the relationship between the force, charge, and distance in the context of Coulomb's law. Coulomb's law states that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Let's examine each scenario and determine the specific changes in the electrostatic force:

a. The charge on one sphere is reduced by half:
If we reduce the charge on one sphere by half, it means that the product of the charges in the equation will be divided by 2. Therefore, the electrostatic force will also be reduced by half, assuming all other factors remain constant.

b. The charge on both spheres is doubled:
If we double the charge on both spheres, it means the product of their charges in the equation will be multiplied by 2. Therefore, the electrostatic force will also be doubled, assuming all other factors remain constant.

c. The distance between the spheres is increased by a factor of three:
If we increase the distance between the spheres by a factor of three, it means the square of the distance in the equation will be multiplied by 3 squared (9). Therefore, the electrostatic force will decrease by a factor of 1/9, or approximately 0.111, assuming all other factors remain constant.

d. The distance between the spheres is decreased to one-fourth:
If we decrease the distance between the spheres to one-fourth, it means the square of the distance in the equation will be multiplied by 1/4 squared (1/16). Therefore, the electrostatic force will increase by a factor of 16, assuming all other factors remain constant.

e. The charge of each sphere is doubled, and the distance between them is doubled:
If we double the charge of each sphere and double the distance between them, it means the product of their charges in the equation will be quadrupled (multiplied by 2*2 = 4), and the square of the distance will also be quadrupled (multiplied by 2*2 = 4). Therefore, the electrostatic force will remain the same, assuming all other factors remain constant.

Remember, these changes in electrostatic force are specific to the given scenarios and assume all other factors remain constant. Coulomb's law provides a quantitative relationship, allowing us to predict the changes in the electrostatic force based on changes in charge and distance.