Final answer:
The force exerted on the center object is zero because the forces exerted by the positive and negative charges cancel each other out.
Step-by-step explanation:
To find the force exerted on the center object, we will use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, the center charge is being acted upon by the positive charge on the left and the negative charge on the right. The force exerted by the left charge is given by:
F_left = k * q_left * q_center / d^2
where k is the electrostatic constant (9 x 10^9 N m^2/C^2), q_left is the charge of the left object (100 nC = 100 x 10^(-9) C), q_center is the charge of the center object (100 nC), and d is the separation between the left and center objects (0.3 m).
Using these values, we can calculate the force exerted by the left charge as:
F_left = (9 x 10^9 N m^2/C^2) * (100 x 10^(-9) C) * (100 x 10^(-9) C) / (0.3 m)^2 = 3 x 10^(-2) N
Similarly, the force exerted by the right charge is given by:
F_right = k * q_right * q_center / d^2
where q_right is the charge of the right object (-100 nC), and using the same values as before, we can calculate the force exerted by the right charge as:
F_right = (9 x 10^9 N m^2/C^2) * (-100 x 10^(-9) C) * (100 x 10^(-9) C) / (0.3 m)^2 = -3 x 10^(-2) N
Since force is a vector quantity, the net force on the center charge is the vector sum of the forces exerted by the left and right charges. Since the forces have equal magnitude but opposite direction, the net force is:
Net force = F_left + F_right = (3 x 10^(-2) N) + (-3 x 10^(-2) N) = 0 N
Therefore, the force exerted on the center object is zero.