Question

The force on a current-carrying wire is a maximum when the current is moving parallel to a magnetic field. true or false

Answer 1

The force is given by F=iL×B  where i is current, L is the path the current follows (the wire path) and B is the magnetic field.  Also recall that the × symbol is the vector cross product, which can be expressed by the sine of the angle between the vectors L and B.  Therefore we can also say F=iLBsin(θ).  Do you know what value of θ makes sin(θ) the largest?  This will tell you if parallel or perpendicular makes the force strongest.  For one value of θ it will be zero, and for the other it will be maximized.