two charges originally separated by 10cm are moved further apart untill the force between them has decreased by a factor of 10. How far apart are these charges?

To find the distance between the charges after the force has decreased by a factor of 10, we can use Coulomb's Law.

Coulomb's Law states that the force (F) between two charges (q1 and q2) is directly proportional to the product of their magnitudes (|q1| and |q2|) and inversely proportional to the square of the distance (r) between them.

Mathematically, Coulomb's Law can be written as:

F = k * (|q1| * |q2|) / r^2

where k is the electrostatic constant.

Now, let's assume the original distance between the charges is represented as r1, and the final distance is represented as r2. The problem states that the force between the charges has decreased by a factor of 10.

This means that r2 (final distance) is increased in such a way that the force becomes 1/10th of its original value.

So, we have:

F_original = k * (|q1| * |q2|) / r1^2

and

F_final = k * (|q1| * |q2|) / r2^2

Given that F_final = 1/10 * F_original, we can write:

k * (|q1| * |q2|) / r2^2 = 1/10 * (k * (|q1| * |q2|) / r1^2)

Cancelling out similar terms, we get:

r2^2 = (r1^2) * 10

Taking the square root of both sides, we find:

r2 = sqrt(10) * r1

Hence, the distance between the charges after the force has decreased by a factor of 10 is √10 (approximately 3.162) times the original distance.

To calculate the actual distance, you need to know the original distance (r1) between the charges.