Ask AI: The force between two 0.003C charges is 1.5N. What is the distance between them?

To determine the distance between two charges given the force between them, we can use Coulomb's law, which describes the electrostatic force between two point charges. Coulomb's law is given by the formula: \[ F = k \frac{|q_1 q_2|}{r^2} \] where: - \( F \) is the magnitude of the force between the charges (in newtons), - \( k \) is Coulomb's constant \((8.99 \times 10^9 \, \text{N}\cdot \text{m}^2/\text{C}^2)\), - \( q_1 \) and \( q_2 \) are the magnitudes of the charges (in coulombs), - \( r \) is the distance between the charges (in meters). Given: \( F = 1.5 \, \text{N} \), \( q_1 = q_2 = 0.003 \, \text{C} \). We need to solve for \( r \). Rearrange the formula to solve for \( r \): \[ r^2 = k \frac{|q_1 q_2|}{F} \] Substitute the known values into the equation: \[ r^2 = 8.99 \times 10^9 \frac{(0.003)^2}{1.5} \] Calculate the values: 1. Calculate \( (0.003)^2 = 0.000009 \). 2. Substitute into the formula: \[ r^2 = 8.99 \times 10^9 \times \frac{0.000009}{1.5} \] 3. Calculate the division: \[ \frac{0.000009}{1.5} = 0.000006 \] 4. Now substitute into the equation: \[ r^2 = 8.99 \times 10^9 \times 0.000006 \] 5. Calculate: \[ r^2 = 8.99 \times 10^9 \times 0.000006 = 53,940 \] 6. Finally, take the square root to solve for \( r \): \[ r = \sqrt{53,940} \approx 232.26 \, \text{m} \] So, the distance between the charges is approximately 232.26 meters.

The force (F) between two charges is given by the formula: F = k*|q1*q2|/r² where: - F is the force between the charges, - k is Coulomb's constant, approximately equal to 9.0 × 10^9 Nm²/C², - q1 and q2 are the amounts of charge, - r is the distance between the charges. In your case, you know the force (1.5N) and the charges (0.003C each), and you need to find r. Rearranging formula: r² = k * |q1 * q2| / F Substituting given/correct values: r² = (9.0 × 10^9 Nm²/C² * |0.003C * 0.003C|) / 1.5N After calculating the above, r = sqrt(r²) Also note: Since the charges q1 and q2 are likely the same type (either positive or negative), their product will be a positive number, so the absolute value isn't strictly necessary.