Two point charges have a total charge of 262 . When placed 1.96 apart, the force each exerts on the other is 18.3 and is repulsive.

What is the charge on each

To determine the charge on each point charge, we can use Coulomb's Law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Let's denote the charge of one of the point charges as q, and the charge of the other point charge as Q. We know that the force between them is repulsive, so the charges must have the same sign (both positive or both negative).

According to Coulomb's Law formula, the force F between two point charges q and Q can be calculated as:

F = (k * |q| * |Q|) / r^2

Here, k is the Coulomb's constant (k ≈ 8.99 × 10^9 N•m^2/C^2), and r is the distance between the charges.

In this case, we have the following information:
- Total charge of the two point charges: 262 C
- Distance between the point charges: 1.96 m
- Force between the point charges: 18.3 N

Since the forces are equal in magnitude, we can set up the following equation:

18.3 = (k * |q| * |Q|) / (1.96^2)

Now, let's rearrange the equation to solve for the product of the charges (|q| * |Q|):

|q| * |Q| = (18.3 * 1.96^2) / k

Substituting the values of k = 8.99 × 10^9 N•m^2/C^2 and r = 1.96 m, we can calculate the product of the charges:

|q| * |Q| = (18.3 * 1.96^2) / (8.99 × 10^9)

|q| * |Q| ≈ 0.08335

Since the charges have the same magnitude, we can divide this product by 2:

|q| = |Q| ≈ 0.08335 / 2

Therefore, the charge on each point charge is approximately 0.0417 C.