When point charges q1=+8.4uC and q2=+5.6uC are brought near each other, each experiences a repulsive force of magnitude 0.66N. Determine the distance between the charges.
To determine the distance between the charges, we can use Coulomb's Law, which relates the magnitude of the electric force between two point charges to their charges and the distance between them.
Coulomb's Law states that the magnitude of the electric force (F) between two point charges can be calculated using the following formula:
F = k * (|q1 * q2|) / r^2
Where:
- F is the magnitude of the electric force
- k is the electrostatic constant, which is approximately equal to 9 x 10^9 N·m²/C²
- q1 and q2 are the charges of the two point charges
- r is the distance between the two point charges
In this case, the magnitude of the electric force experienced by each charge is given as 0.66 N. The charges are q1 = +8.4 μC and q2 = +5.6 μC.
Now, let's rearrange the formula to solve for the distance (r):
r^2 = (k * |q1 * q2|) / F
Plugging in the given values:
r^2 = (9 x 10^9 N·m²/C² * |(8.4 x 10^-6 C) * (5.6 x 10^-6 C)|) / 0.66 N
Simplifying:
r^2 = [(9 x 10^9 N·m²/C²) * (8.4 x 10^-6 C) * (5.6 x 10^-6 C)] / 0.66
r^2 = (42.336 x 10^-6 N·m²/C²) / 0.66
r^2 ≈ 64 x 10^-6 N·m²/C²
Taking the square root to solve for r:
r ≈ √(64 x 10^-6 N·m²/C²)
r ≈ 8 x 10^-3 m
Therefore, the distance between the charges is approximately 8 millimeters (8 mm).