Answer: To calculate the magnitude of the electric charge of the second object, we can use Coulomb's Law, which relates the electrostatic force between two charged objects to the product of their charges and the distance between them.
Coulomb's Law formula for the electrostatic force (F) between two charged objects is given by:
F = k * (|q1 * q2|) / r^2
where:
F = electrostatic force (in Newtons)
k = Coulomb's constant (approximately 8.99 × 10^9 N m²/C²)
q1 and q2 = charges of the two objects (in Coulombs)
r = distance between the centers of the two objects (in meters)
Given data:
Distance (r) = 50 cm = 0.5 m
Electrostatic force (F) = 0.29 N
Charge of the first object (q1) = +4 nC = +4 × 10^-9 C
Now, we need to find the magnitude of the charge (q2) on the second object. Rearrange Coulomb's Law to solve for q2:
|q2| = (F * r^2) / (k * |q1|)
Substitute the known values:
|q2| = (0.29 N * (0.5 m)^2) / (8.99 × 10^9 N m²/C² * |4 × 10^-9 C|)
|q2| = (0.29 N * 0.25 m²) / (8.99 × 10^9 N m²/C² * 4 × 10^-9 C)
|q2| ≈ 2.58 × 10^-10 C
Finally, the magnitude of the electric charge of the second object is approximately 2.58 × 10^-10 Coulombs.