Final answer:
The approximate value of q is 2F.
Step-by-step explanation:
The net force on the middle charge can be found by summing up the forces exerted by the two outer charges on the middle charge. According to Coulomb's law, the force between two charges is given by F = k * (|q1*q2| / r^2), where k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.
Since the net force is given as F, we can set up the equation:
F = k * (|q1*q2| / r^2) + k * (|q3*q2| / r^2)
Substituting the known values, the equation becomes:
F = k * (|q*q| / r^2) + k * (|-3q*q| / r^2)
Simplifying further, we get:
F = k * q^2 / r^2 * (1 - 3)
Therefore, the force is proportional to q^2. If the force is F and we replace q with 2q, the new force would be 4F. Therefore, the approximate value of q is 2F (option A).