Final answer:
The value of charge q3 for a net force of 3.00 µN can be found using Coulomb's Law, taking into account both q1 and q2 and their distances from q3.
To find a point on the x-axis where the net force on q3 is zero, one must set an equilibrium condition and solve the resulting equations. The problem requires understanding of electric forces and equilibrium in an electric field.
Step-by-step explanation:
To determine the value of charge q3 for the net force on it to be 3.00 µN, we apply Coulomb's Law which states that the force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.
For the net force to be zero on q3 located at the origin, the forces due to q1 and q2 must be equal in magnitude and opposite in direction. Using the superposition principle, the total force on q3 is the vector sum of the forces due to q1 and q2.
For the second part of the question, the specific location along the x-axis other than infinity where the net force on q3 would be zero, requires setting up an equilibrium condition for the forces exerted by q1 and q2 on q3.
This involves finding a point where the magnitudes of these forces are equal, which can be determined by setting up the equation for forces and solving for the position.
To find a trivial case where the net force on q3 is zero, the point where forces due to the other charges cancel each other out could be at the midpoint of q1 and q2 for symmetrical charge distributions, but in this asymmetrically charged system, it requires further calculation.