Answer: the separation between the two charges is approximately 111.70 meters.
Step-by-step explanation:
To find separation between the two charges, we can use Coulomb's Law,
Coulomb's Law equation:
F = k * |q1 * q2| / r^2
Given:
Charge q1 = -35.0 μC (microCoulombs)
Charge q2 = +101 μC (microCoulombs)
Force F = 4.00 N
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
Rearranging the equation to solve for separation distance (r):
r = sqrt(k * |q1 * q2| / F)
Plugging in the values:
r = sqrt((8.99 x 10^9 N m^2/C^2) * |(-35.0 μC) * (+101 μC)| / 4.00 N)
r = sqrt((8.99 x 10^9 * 35.0 * 101) / 4.00) m
r ≈ 111.70 meters
Therefore, the separation between the two charges is approximately 111.70 meters.