Final answer:
Using Coulomb's law, we can find that the two small charged spheres, which are initially 6.47 cm apart, are now approximately 11.43 cm apart when the force on each of them is tripled.
Step-by-step explanation:
To solve this problem, we can use Coulomb's law, which relates the force between two charges to the distance between them. Coulomb's law states that the force between two charges is directly proportional to the product of the charges, and inversely proportional to the square of the distance between them.
We are given that the initial force between the charges is 5.00 N when they are 6.47 cm apart. We can set up the equation as follows:
F_initial = k * (q1 * q2) / d^2
where F_initial is the initial force, k is the electrostatic constant, q1 and q2 are the charges on the spheres, and d is the initial distance between the spheres.
Let's call the initial distance d1 and the initial force F1. We know that F1 = 5.00 N and d1 = 6.47 cm. We can then rearrange the equation to solve for k:
k = F1 * d1^2 / (q1 * q2)
Now, let's consider the new situation where the force on each sphere has been tripled. Let's call the new distance d2 and the new force F2. Since the force is directly proportional to the charges and inversely proportional to the square of the distance, we can write the equation as follows:
F2 = 3 * F1 = 3 * (k * (q1 * q2) / d2^2)
Dividing both sides of the equation by F1, we get:
3 = k * (q1 * q2) / d2^2
Now, we can substitute the value of k that we solved for earlier:
3 = (F1 * d1^2 / (q1 * q2)) * (q1 * q2) / d2^2
Cancelling out the terms and rearranging the equation, we find:
d2^2 = (F1 * d1^2) / 3
Taking the square root of both sides and rounding to the appropriate number of significant figures, we get:
d2 = sqrt((F1 * d1^2) / 3)
Substituting the given values into the equation, we find that d2 is approximately 11.43 cm.