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:
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
F = k q1q2/r^2
See what happens, for example a) make q1, q1/2
To understand what happens to the electrostatic force in each scenario, we need to consider the variables involved: the charge on the spheres and the distance between them. The electrostatic force between two charged spheres is given by Coulomb's Law, which states that the force is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
a. If the charge on one sphere is reduced by half:
To calculate the change in electrostatic force, we consider that the force is directly proportional to the product of their charges. Therefore, reducing the charge on one sphere by half will cause a proportional reduction in the electrostatic force between them. So, the electrostatic force will also be reduced by half.
b. If the charge on both spheres is doubled:
Again, considering that the force is directly proportional to the product of their charges, doubling the charge on both spheres will result in a proportional increase in the electrostatic force between them. Thus, the electrostatic force will also be doubled.
c. If the distance between the spheres is increased by a factor of three:
Since the electrostatic force is inversely proportional to the square of the distance between the spheres, increasing the distance by a factor of three will result in a proportional decrease in the force. The square of three is nine, so the electrostatic force will decrease by a factor of nine.
d. If the distance between the spheres is decreased to one-fourth:
Similarly, decreasing the distance to one-fourth of the initial value will cause an inverse relationship. The square of one-fourth is one-sixteenth, so the electrostatic force will increase by a factor of sixteen.
e. If the charge of each sphere is doubled and the distance between them is doubled:
Doubling the charge on each sphere will result in a proprotional increase in the electrostatic force, as mentioned earlier. However, doubling the distance will cause a significant decrease, as the force is inversely proportional to the square of the distance. So, the increase in charge will result in a doubling of the force, while doubling the distance will cause a decrease in force by a factor of four. The net effect will be a decrease in the electrostatic force by a factor of two.
In summary:
a. The electrostatic force will be reduced by half.
b. The electrostatic force will be doubled.
c. The electrostatic force will decrease by a factor of nine.
d. The electrostatic force will increase by a factor of sixteen.
e. The electrostatic force will decrease by a factor of two.