The electrostatic force between two charges is originally F. Which expression represents the new electrostatic force between the two charges if one charge doubles and the other one is divided by three?
1/6F
2/3F***
6F
3/2F
correct
To find the new electrostatic force between the two charges, we need to consider how changes in the charges affect the force. The electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Let's assume the original charges are Q1 and Q2, and the original force is F.
Given that one charge doubles (2Q1) and the other charge is divided by three (Q2/3), we need to determine the new force (F').
The new force (F') can be calculated using the following formula:
F' = k * (2Q1) * (Q2/3) / d^2
Where:
- k represents the electrostatic constant
- d represents the distance between the charges
Since we are comparing the new force to the original force, we can simplify the calculation by dividing the existing terms by F, giving us:
F' / F = (k * (2Q1) * (Q2/3) / d^2) / F
Now, we can substitute the expression for the new charge values and simplify:
F' / F = (k * (2Q1) * (Q2/3) / d^2) / F
= (2/3) * k * (Q1 * Q2) / (d^2 * F)
From the above expression, we can see that the new electrostatic force (F') divided by the original force (F) is equal to (2/3) * k * (Q1 * Q2) / (d^2 * F).
Therefore, the correct expression representing the new electrostatic force between the two charges is 2/3F.