Two charged spheres are 18.0 cm apart. They are moved, and the force on each of them is found to have been doubled. How far apart are they now?
______cm
According to the inverse square law that applies to electrostatic forces, the separation distance must decrease by a factor sqrt2 if the force is to increase by a factor of two.
18/sqrt2 = 12.7 cm
To find the new distance between the two charged spheres, we can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's consider the initial situation to be Sphere A and Sphere B separated by a distance of 18.0 cm. The force between them is F1.
Now, let's assume that the spheres are moved so that they are now a certain distance apart (let's call it x). The force between them is now twice the initial force, which we can call F2.
According to Coulomb's Law, we can write the equation:
F1 / F2 = (d2)^2 / (d1)^2
where d1 is the initial distance (18.0 cm), d2 is the new distance (x), and F1 and F2 are the initial and new forces, respectively.
Since we are given that the new force is twice the initial force (F2 = 2F1), we can substitute these values into the equation:
F1 / (2F1) = (x)^2 / (18.0 cm)^2
Simplifying the equation, we have:
1/2 = (x)^2 / (18.0 cm)^2
To solve for x, we can multiply both sides of the equation by (18.0 cm)^2:
(x)^2 = (1/2) * (18.0 cm)^2
(x)^2 = 162 cm^2
Taking the square root of both sides, we find:
x = √(162 cm^2)
x ≈ 12.73 cm
Therefore, the two charged spheres are now approximately 12.73 cm apart.