Final answer:
The correct relationship between q1 and q2 for the net electrostatic force on a third charge at the origin to be zero is q2 = -4q1, according to Coulomb's law and the inverse square relationship with distance.
Step-by-step explanation:
For the net electrostatic force on a third charged particle located at the origin to be zero, the forces exerted by particles 1 and 2 must be equal in magnitude but opposite in direction. According to Coulomb's law, the force exerted by a charge is directly proportional to the product of the charges and inversely proportional to the square of the distance between them, F = k|q1*q2|/r². Since the distances from the origin to the particles are a and 2a for particle 1 and 2 respectively, and knowing that the force exerted is inversely proportional to the square of the distance, we can set up the proportion k|q1*q3|/a² = k|q2*q3|/(2a)² where q3 is the charge of the third particle. Simplifying, we get |q2| = 4*|q1|, which implies that q2 must be four times q1, but with the opposite sign, since the charges must exert forces in opposite directions. Therefore, the correct answer is B. q2 = -4q1.