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:
The charge on one sphere is reduced by half
The charge on both spheres is doubled
The distance between the spheres is increased by a factor of three
The distance between the sphere is decreased to one-fourth
The charge of each sphere is doubled and the distance between them is doubled
Here is an equation called Coulomb's Law that might help you find the answers:
Force of electricity=
k x (q1 x q2)/r^2
k= Coulomb's constant= 9x10^9
q1= charge 1
q2= charge 2
r= distance between two charges
Just plug in numbers to the equation and find the force. Then, change the numbers according to to your given situations and find the new force. Compare the new force with the original force and describe the change. Good Luck with your homework.☻
To answer the question, we need to understand the relationship between electrostatic force, charge, and distance. The electrostatic force between two charged spheres can be calculated using Coulomb's law:
F = k * (q1 * q2) / r^2
where F is the electrostatic force, k is the electrostatic constant, q1 and q2 are the charges on the spheres, and r is the distance between the spheres.
Now, let's analyze each scenario:
1. The charge on one sphere is reduced by half:
In this case, only one of the charges is changed. Let's say the charge on sphere 1 is reduced by half. As a result, the force between the spheres would decrease. This is because the electrostatic force is directly proportional to the product of the charges. So, if one of the charges is reduced, the force will decrease.
2. The charge on both spheres is doubled:
When both charges are doubled, the force between the spheres would increase. Again, this is due to the direct proportionality between the charges and the force.
3. The distance between the spheres is increased by a factor of three:
Increasing the distance between the spheres would result in a decrease in the force between them. This decrease occurs because the electrostatic force is inversely proportional to the square of the distance. By increasing the distance by a factor of three, the force between the spheres would decrease by a factor of (1/3)^2 = 1/9.
4. The distance between the spheres is decreased to one-fourth:
Decreasing the distance between the spheres would lead to an increase in the force between them. This increase happens because the electrostatic force is inversely proportional to the square of the distance. By decreasing the distance to one-fourth, the force between the spheres would increase by a factor of (4^2) = 16.
5. The charge of each sphere is doubled, and the distance between them is doubled:
In this scenario, both the charges and the distance between the spheres are doubled. Doubling the charges would result in an increase in force, as explained earlier. However, doubling the distance would cause the force to decrease by a factor of (2^2) = 4. So, the overall effect on the force would depend on the magnitude of these changes, but mathematically, the force would decrease due to the increase in distance.
Remember, these explanations are based on the assumptions made in Coulomb's law and assume no other external factors are at play.