The force of repulsion that two like charges exert on each other is 3.2 N. What will the force be if the distance between the charges is increased to 4 times its original value?

To solve this problem, we can use Coulomb's Law, which states that the force of repulsion between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2

Where:
F is the force of repulsion,
k is the electrostatic constant (9.0 × 10^9 N m^2/C^2),
q1 and q2 are the charges of the two objects, and
r is the distance between the charges.

In this case, we are given that the force of repulsion is 3.2 N. Let's call this force F1. We want to find the force of repulsion when the distance between the charges is increased by a factor of 4. Let's call this force F2.

We can set up a proportion using Coulomb's Law:

F1 / F2 = (r2^2) / (r1^2)

where r1 is the original distance and r2 is the new distance. We are given that the new distance is 4 times the original distance.

Let's substitute the known values into the proportion:

3.2 N / F2 = (4r1)^2 / r1^2

Simplifying further:

3.2 N / F2 = 16

Now we can solve for F2 by rearranging the equation:

F2 = 3.2 N / 16
F2 = 0.2 N

Therefore, the force of repulsion when the distance between the charges is increased to 4 times its original value will be 0.2 N.

The force of repulsion between two like charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Let's denote the initial force as F1, the initial distance between the charges as d1, and the new distance between the charges as d2.

According to the problem, F1 = 3.2 N.

Now, if we increase the distance between the charges to 4 times its original value, we have d2 = 4 * d1.

The relationship between force and distance can be expressed as:

F1/d1^2 = F2/d2^2

Where F2 is the new force we're trying to find.

Substituting the values we have:

3.2 N / d1^2 = F2 / (4 * d1)^2

Simplifying:

3.2 N / d1^2 = F2 / 16 * d1^2

Cross-multiplying:

3.2 N * 16 * d1^2 = F2 * d1^2

51.2 = F2

Therefore, the force will be 51.2 N if the distance between the charges is increased to 4 times its original value.