To solve this problem, we can use the formula for electric potential energy:
Electric potential energy (U) = (k * q1 * q2) / r
Where:
- k is the Coulomb constant (k = 8.98755 x 10^9 N · m^2/C^2)
- q1 and q2 are the charges of the two spheres
- r is the distance between the spheres
In this case, q1 is the charge removed from the first sphere (-1 x 10^13 electrons) and q2 is the charge added to the second sphere (+1 x 10^13 electrons).
First, we need to calculate the charges in Coulombs:
Charge in Coulombs = (charge in electrons) * (charge of an electron)
q1 = (-1 x 10^13) * (1.6 x 10^-19 C) = -1.6 x 10^-6 C
q2 = (1 x 10^13) * (1.6 x 10^-19 C) = 1.6 x 10^-6 C
Substituting the values into the formula:
-0.061 J = (8.98755 x 10^9 N · m^2/C^2) * (-1.6 x 10^-6 C) * (1.6 x 10^-6 C) / r
Rearranging the equation to solve for r:
r = (8.98755 x 10^9 N · m^2/C^2) * (-1.6 x 10^-6 C) * (1.6 x 10^-6 C) / -0.061 J
Calculating this expression:
r ≈ 0.687 meters
Therefore, the distance between the two spheres is approximately 0.687 meters.