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.