A magnetic field problem, everyone come to see, their own drawings

Analysis: when the AB side will be out of the magnetic field (but still in the magnetic field), the total electric potential of the circuit is maximum, the current is also maximum, the amperage force is also maximum, due to uniform motion, then the corresponding external force is also maximum.

See, in the external force is maximum, only the AB side of the electric potential (AC side can be considered out of the magnetic field, no electric potential).

The electric potential generated on the AB side is E = BLV

The current is I = E / R

The amperometric force is F amp = B*I*L = (BL)^2 * V / R

So the maximum value of the external force is F externally large = (BL)^2 * V / R

Note: The result you gave is wrong.