Final answer:
Using Coulomb's law, we find that the magnitude of each charge is approximately 2.9 µC to achieve the specified attractive force of 10 N over a separation of 6.4 cm.
Step-by-step explanation:
The student wants to know the magnitude of each charge in a pair that is separated by 6.4 cm and exerts an attractive force of 10 N on one another.
To find this, we use Coulomb's law, which is stated as F = k * |q1 * q2| / r^2, where F is the force between the charges, k is Coulomb's constant (8.988 × 10^9 N·m²/C²), q1 and q2 are the magnitudes of the charges, and r is the separation between the charges.
Assuming the charges have equal magnitude, we can set q1 = q2 = q and rearrange the equation to solve for q: q = √(F * r^2 / k). Plugging in the given values, we first convert the distance to meters: 6.4 cm = 0.064 m.
The equation becomes q = √(10 N * (0.064 m)^2 / (8.988 × 10^9 N·m²/C²)). Calculating this, we get q ≈ 2.88 × 10^-6 C, or 2.9 µC to two significant figures.