Final answer:
To achieve zero net electrostatic force on a third charge at the origin, the second charge must be placed on the x-axis at a specific distance where its force on the third charge cancels the force from the first charge, as determined by Coulomb's Law.
Step-by-step explanation:
The original question pertains to the placement of a charge to create a resultant zero net electrostatic force on a third charge located at the origin. In resolving these types of problems, we utilize Coulomb's Law, which states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. To achieve zero net force on the third charge, q3, we must position the second charge, q2, at a distance where its electrostatic force on q3 would exactly cancel the electrostatic force exerted by q1 on q3.
Let's consider the distance to be x from the origin on the x-axis, but in the direction opposite to that of q1, since q2 is negative and would thus exert an attractive force on the positive q3 at the origin. The magnitudes of the forces due to q1 and q2 on q3 must be equal for the net force to be zero. Using the relationship for electrostatic force given by Coulomb's Law, this can be set up as an equation, and we can solve for the distance x at which q2 should be placed.