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 determine how far apart the two charged spheres are now, we need to consider Coulomb's Law, which relates the force between two charged objects to their charges and the distance between them. The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
- F is the electric force between the two charged objects
- k is the electrostatic constant (k ≈ 9 × 10^9 N m^2/C^2)
- q1 and q2 are the charges of the two objects
- r is the distance between the centers of the objects
Let's assume the original force between the two spheres was F1, and the final force after they were moved is F2. We can use the ratio of the forces to find the new distance between the spheres.
Since the force on each sphere is tripled, we have:
F2 = 3 * F1
Now, we can equate the formulas for electric force:
k * (q1 * q2) / r2^2 = 3 * (k * (q1 * q2) / r1^2)
Notice that q1 and q2 cancel out, as they are the same for both spheres. Also, we'll assume the charges q1 and q2 are still the same after the spheres are moved.
Simplifying the equation:
r2^2 = 3 * r1^2
To determine the new distance, we need to solve for r2. Taking the square root of both sides:
r2 = √(3 * r1^2)
Now, we can substitute the given value of r1 (which is 5.25) into the equation to find r2:
r2 = √(3 * 5.25^2) ≈ 7.22
Therefore, the two charged spheres are approximately 7.22 units apart after being moved, given that the force on each of them is found to have been tripled.
To find the new distance between the two charged spheres, we can use the inverse square law of electric force, which states that the force between two charged objects is inversely proportional to the square of the distance between them.
Let's call the initial distance between the spheres d1, and the final distance between the spheres d2.
According to the problem, the force on each sphere is tripled when the spheres are moved. This means the new force (F2) is three times the initial force (F1).
Since the electric force is inversely proportional to the square of the distance, we can write the following relationship:
F1 / F2 = (d2 / d1)^2
Substituting the given information into the equation, we have:
1 / 3 = (d2 / 5.25)^2
Taking the square root of both sides of the equation gives us:
√(1 / 3) = d2 / 5.25
Simplifying this equation further, we get:
√(1 / 3) * 5.25 = d2
Now, let's calculate the final distance between the spheres.
d2 ≈ √(1 / 3) * 5.25 ≈ 3.037
The final distance between the charged spheres, after the force on each of them has been tripled, is approximately 3.037 units.