Final answer:
Yes, it is possible to place two point charges along the x-axis so the electric field at the origin is zero by positioning them at specific distances from the origin, where the electric fields they produce are equal in magnitude but opposite in direction.
Step-by-step explanation:
The student is asking whether it is possible to arrange two point charges along the x-axis so that the resultant electric field (E) is zero at the origin. In this scenario, we have charge q1 with a value of -2.0×10-6C and charge q2 with a value of 4.0×10-6C.
To achieve an electric field of zero at the origin, we would need to position these charges so that the electric fields produced by each charge cancel each other out. The electric field (E) due to a point charge is given by Coulomb's law as E = k|q|/r2, where k is Coulomb's constant (8.99×109 Nm2/C2), q is the charge, and r is the distance from the charge to the point of interest.
For the electric field at the origin to be zero, the field created by q1 must be equal in magnitude but opposite in direction to that created by q2. Given that the magnitudes of the charges are different, we'll need to place them at different distances from the origin to achieve this balance. By setting up the equation k|q1|/r12 = k|q2|/r22 and solving for the ratios of distances (r1 and r2) that satisfy this relation, we can find the precise positions for both charges.