The direction of the force on a current-carrying wire in a magnetic field is

The forces acting on a conductor carrying current placed in a magnetic field is analysed using the Fleming's left hand rule.

The rule states that "If the fire finger, the middle finger and the thumb are held mutually perpendicular to one another in a magnetic field, the fore finger acts in the direction of the magnetic field, the middle finger acts on the direction of the current while the thumb acts in the direction of the force.

Based on the rule, it can be inferred this current carrying wire placed in the magnetic field acts perpendicular to the magnetic field and force acting on the wire.

The force that a particle of charge q and velocity v experiences when entering an electromagnetic field is:

F = q * (E + vxB)

Where E is the electric field and B is the magnetic field, here we only care for the magnetic field.

From this, we can see that the magnetic force will be perpendicular to the velocity and the magnetic field, and knowing that in a cable the electrons flow along the wire, we have that the force must be perpendicular to the wire and also to the magnetic field in where the wire is.