Two small charged balls have a repulsive force of 0.20N when they are separated by a distance of 0.90m . The balls are moved closer together, until the repulsive force is 0.58N .

How far apart are they now?

Express your answer to two significant figures and include the appropriate units.

Now wait a minute, your questions are really all the same question. The only difference is arithmetic.

F = k Q1Q2 /r^2

To find the new distance between the two charged balls, we can use the concept of Coulomb's Law. Coulomb's Law 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 assume the initial charges on the balls are q1 and q2, and the initial distance between them is r1. The initial force between the balls (F1) is given as 0.20N.

Similarly, let's assume the new charges on the balls are q1 and q2, and the new distance between them is r2. The new force between the balls (F2) is given as 0.58N.

According to Coulomb's Law:

F1 = k * (q1 * q2) / r1^2

F2 = k * (q1 * q2) / r2^2

where k is the Coulomb constant.

Dividing the two equations, we get:

F2 / F1 = (r1 / r2)^2

We can rearrange the equation to solve for r2:

r2 = r1 * sqrt(F1 / F2)

Substituting the given values, we have:

r2 = 0.90m * sqrt(0.20N / 0.58N)

Simplifying:

r2 = 0.90m * sqrt(0.34)

r2 ≈ 0.90m * 0.583

r2 ≈ 0.5247m

Therefore, the balls are now approximately 0.52m apart.

To find the new distance between the two charged balls, we need to use Coulomb's Law. Coulomb's Law 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 me break down the steps to find the new distance:

Step 1: Identify the given information:
- Initial force, F1 = 0.20 N
- Initial distance, r1 = 0.90 m
- Final force, F2 = 0.58 N

Step 2: Set up the equation using Coulomb's Law:
F1/F2 = (r2^2)/(r1^2)

Step 3: Rearrange the equation to solve for the new distance, r2:
r2^2 = (F2/F1) * (r1^2)
r2 = √((F2/F1) * (r1^2))

Step 4: Substitute the given values into the equation and calculate the new distance, r2:
r2 = √((0.58 N / 0.20 N) * (0.90 m)^2)
r2 = √2.61 * 0.81 m
r2 = √2.115
r2 ≈ 1.45 m

Therefore, the new distance between the two charged balls is approximately 1.45 meters.