Explanation:
The rod moving in a magnetic field and induces an emf which is used to illuminate the bulb. But if the bulb is removed form the circuit, the circuit is opened.
For an open circuit, no current is passes through the moving rod. If there is no current along the rod, then no magnetic field developed around the rod. Because moving charges nothing but current produces the magnetic field around the rod.
The formula for the magnetic force on the rod is,
[tex]F_{\mathrm{B}} &=I(l \times B)[/tex]
[tex]=I l B \sin \theta[/tex]
The current along the rod is zero because the bulb is removed and the magnetic field around the rod is zero because no current is passes through the rod.
Then calculate the magnetic force on the rod as follows:
\[tex]F_{\mathrm{B}} &=I l B \sin \theta[/tex]
[tex]=(0)(l)(0) \sin \theta =0 \mathrm{N}[/tex]
Thus, no force is needed because there is no longer magnetic field developed around the rod.
