Answer
$(a) 0N$
Work Step by Step
Assuming there is magnetic field in the region represented by red cross
Here external force is required because magnetic field exerts a force on the current carrying rod opposite to the force applied by external agent.
Now when bulb is unscrewed the circuit breaks and thus there is no current flow, so no force will be exerted by magnetic field on the rod; that implies no external force is required to keep it moving with constant speed.
Therefore answer is $0 N$
