Two identical small spheres possessing charges q1 and q2 are separated by distance r. Which change would produce the greatest increase in the magnitude of the electrostatic force that one sphere exerts on the other?
1) doubling charge q1
2) doubling r
3) doubling r and charge q1
4) doubling r and charges q1 and q2
the answer is 1 but why?
The end goal is to incrase but if r is doubled, because it is a denominator, the answer would turn out to be small
Well, let me shed some light on this electrifying question for you! When it comes to increasing the magnitude of the electrostatic force between two charged spheres, the key factor to consider is the product of the charges involved and the square of the distance between them.
In this scenario, doubling charge q1 would indeed result in the greatest increase in the electrostatic force. This is because the force between two charged objects is directly proportional to the product of their charges. By doubling the charge of q1, we effectively double the product of the charges, leading to a significant increase in the force exerted.
On the other hand, doubling the distance (option 2) would actually result in a decrease in the electrostatic force. This is because the force between two charges is inversely proportional to the square of the distance between them. So increasing the distance would lead to a weaker force.
As for options 3 and 4, doubling both the distance and the charges wouldn't have as significant of an impact as doubling only charge q1. While these changes would result in an increase in the force, doubling charge q1 alone would still have a bigger effect on the magnitude of the force.
So, in a shocking turn of events, the answer is indeed option 1 - doubling charge q1. It's like giving your sphere a charge upgrade!
The greatest increase in the magnitude of the electrostatic force can be achieved by doubling the charge q1.
The magnitude of the electrostatic force between two charges is given by Coulomb's Law equation:
F = k * (q1 * q2) / r^2,
where F is the magnitude of the electrostatic force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.
When we double the charge q1, the new electrostatic force becomes:
F' = k * (2 * q1 * q2) / r^2,
The ratio of the new force F' to the original force F is:
F'/F = [k * (2 * q1 * q2) / r^2] / [k * (q1 * q2) / r^2]
= (2 * q1 * q2) / (q1 * q2)
= 2.
This shows that the new force F' is twice as large as the original force F. Therefore, doubling the charge q1 will produce the greatest increase in the magnitude of the electrostatic force that one sphere exerts on the other.
To determine which change would produce the greatest increase in the magnitude of the electrostatic force between the two spheres, we need to understand the mathematical relationship between the force and the factors involved.
The electrostatic force between two charges is given by Coulomb's Law:
F = (k * q1 * q2) / r^2
Where:
F is the electrostatic force,
k is the electrostatic constant (a fundamental constant),
q1 and q2 are the charges on the two spheres,
and r is the distance between the centers of the two spheres.
Let's analyze each option and see how it affects the force:
Option 1: Doubling charge q1
If we double the charge q1, the force formula becomes:
F' = (k * (2q1) * q2) / r^2
Since q1 is doubled, the numerator of the formula becomes 2 * q1, resulting in an increase in the force.
Option 2: Doubling distance r
If we double the distance r, the force formula becomes:
F' = (k * q1 * q2) / (2r)^2
= (k * q1 * q2) / 4r^2
Doubling the distance squared (2r)^2 results in 4r^2 in the denominator. This means the force will decrease by a factor of 4.
Option 3: Doubling both r and q1
If we double both the distance r and the charge q1, the force formula becomes:
F' = (k * (2q1) * q2) / (2r)^2
= (k * (2q1) * q2) / 4r^2
Doubling both variables still results in the factor of 4 in the denominator, just like in option 2. Therefore, the force will increase, but by the same factor as in option 1, which is simply doubling the charge q1.
Option 4: Doubling both r, q1, and q2
Following the same logic, doubling all the variables still results in the factor of 4 in the denominator:
F' = (k * (2q1) * (2q2)) / (2r)^2
= (k * (2q1) * (2q2)) / 4r^2
Again, the force will increase, but by the same factor as in option 1, which is doubling the charge q1.
From this analysis, we can conclude that doubling the charge q1 would produce the greatest increase in the magnitude of the electrostatic force that one sphere exerts on the other.