When an electric current is flowing through a wire, the force deflecting the charged particles is the greatest when the wire is what to the magnetic field?

The force is greatest when the wire is perpendicular to the magnetic field.

In fact, the expression for the magnetic force is

where I is the current, L the length of the wire, B the magnetic field intensity and is the angle between the directions of I and B.

We can see that F is maximum when , so when , so when the wire and the magnetic field are perpendicular to each other.