Two charged spheres are 5.25 apart. They are moved, and the force on each of them is found to have been tripled. how far apart are they now?
To calculate the new distance between the charged spheres, we need to use the principles of the electric force between charges. The electric force between two charged objects is given by Coulomb's law:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges (initially tripled)
k is the electrostatic constant (a constant value)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
In this case, the force on each sphere has been tripled, so the initial force of F1 is now 3F1, and the initial force of F2 is now 3F2.
Using Coulomb's law, we can set up the following equation to solve for the new distance, r':
(3F1) = k * (q1 * q2) / (r'^2)
(3F2) = k * (q1 * q2) / (r'^2)
Dividing the second equation by the first equation:
(3F2) / (3F1) = (k * (q1 * q2) / (r'^2)) / (k * (q1 * q2) / (r'^2))
The electrostatic constant, k, and the charges, q1 and q2, cancel out:
(3F2) / (3F1) = r'^2 / r'^2
Since the squares of the distances on both sides cancel out, we are left with:
(3F2) / (3F1) = 1
We can conclude that the new distance, r', between the spheres is the same as the initial distance, r, since the ratio of the forces remains the same.
Therefore, the spheres are still 5.25 units apart.