Final answer:
The y-component of the net force on the second charged rod vanishes because the y-components of electric forces from symmetrically opposite charge elements of the first rod cancel each other out due to the system's symmetry, leaving a net force that acts solely along the x-axis.
Step-by-step explanation:
Explanation for the Net Force on the Second Rod
The student is asking why the y-component of the net force on the second rod, which has a charge of +Q and is positioned parallel to another similarly charged rod, vanishes. In electrostatics, the electric force between two charges depends on the magnitude of the charges and their separation distance. Since both rods have the same charge (+Q), they will repel each other. The electric field produced by a uniformly charged rod at points along a line perpendicular to its length is directed radially outward from the rod. As such, at any point along the second rod, the contributions to the electric field from the charge elements of the first rod have a radial component and a component along the y-axis.
Due to the symmetry of the system and the linear charge distributions, the forces due to the y-components from symmetrically opposite charge elements on the first rod will cancel out, leaving no net y-component of force on the second rod. The remaining forces from all the elements have only x-components, which add together to create a net repulsive force acting solely along the x-axis. Thus, the y-component of the net force is zero.