In which of the following cases a straight current-carrying conductor does not experience a force?
When a current-carrying conductor is placed in a magnetic field, a force is exerted on the conductor. The direction of this force is perpendicular to both the direction of current as well as the direction of the magnetic field (Fleming's left-hand rule).
The conductor will not experience a force if the angle between the current and the magnetic field is 0∘ or 180∘, i.e., parallel. In all other cases, it experiences a force.