Two point charges attract each other with an electric force of magnitude F. If one charge is reduced to 1/3 its original value and the distance between the charges is doubled, what is the resulting magnitude of the electric force between them?
No
To determine the resulting magnitude of the electric force, we can use Coulomb's Law, which states that the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's assume the original charges are labeled as q1 and q2, and the original distance between them is labeled as r.
According to Coulomb's Law, the electric force (F) between the two charges is given by:
F = k * (q1 * q2) / r^2
where k is the electrostatic constant.
Now, let's consider the changes in the values given:
1. One charge has been reduced to 1/3 of its original value: q1' = q1 / 3
2. The distance between the charges is doubled: r' = 2 * r
Using these changes, we can find the resulting magnitude of the electric force.
The resulting magnitude of the electric force (F') is given by:
F' = k * (q1' * q2) / r'^2
Substituting the given changes:
F' = k * ((q1 / 3) * q2) / (2 * r)^2
Simplifying further:
F' = (1/12) * (k * q1 * q2) / r^2
Since k * q1 * q2 / r^2 is equal to the original magnitude of the electric force F:
F' = (1/12) * F
Therefore, the resulting magnitude of the electric force between the two charges is 1/12 times the original magnitude, F.
To find the resulting magnitude of the electric force, we can use Coulomb's Law equation:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges
k is the electrostatic constant (k ≈ 8.99 × 10^9 N m^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
Given that the initial force is F, one charge is reduced to 1/3 its original value, and the distance between the charges is doubled, we can make the following substitutions:
Let's assume the original magnitudes of the charges are q1 and q2, and the original distance is r.
New magnitude of the first charge: q1' = (1/3) * q1
New magnitude of the second charge: q2' = q2
New distance between the charges: r' = 2 * r
Now we can calculate the resulting magnitude of the electric force using the modified values:
F' = k * (q1' * q2') / (r')^2
Substituting the corresponding values:
F' = k * [(1/3) * q1] * q2 / (2 * r)^2
Now we can simplify the equation:
F' = k * (1/9) * (q1 * q2) / (4 * r^2)
F' = (1/36) * k * (q1 * q2) / r^2
We can see that the resulting magnitude of the electric force between the charges is 1/36 of the original magnitude F.