The can stays still (it does not roll to either side) when the two rods are equally charged in magnitude and placed at equal distance on opposite sides.

Why the can stays still

  • Each charged rod polarizes the aluminum can, pulling opposite charges on the nearer side and pushing like charges to the farther side.
  • The rod on the left attracts induced charge on the left surface; the rod on the right does the same on the right surface, with equal strength if the charges and distances are the same.
  • Because the setup is perfectly symmetric, the horizontal forces on the can from the two rods are equal in magnitude and opposite in direction, so the net force is zero and the can does not move.

Intuitively, think of the can as being “tugged” equally hard from both sides; it becomes polarized, but those tugs cancel out, so it just sits there.

TL;DR: With two oppositely charged rods of equal magnitude at equal distance from an aluminum can, the induced attractions balance, so the can remains in place and does not roll.

Information gathered from public forums or data available on the internet and portrayed here.