Electromagnetic Induction: Tricky Questions Solved (1)

The current-carrying rod in the field experiences:

This opposes motion (Lenz’s law), so the external force needed is $F_{ext} = 0.125$ N in the direction of motion.

Energy in = energy out. Balance verified.

Final answer: $\varepsilon = 1$ V, $I = 0.5$ A, $F = 0.125$ N, $P = 0.5$ W.

Why This Works

The motional emf $BLv$ comes from the magnetic force on free electrons inside the moving rod. Once current flows, the same field exerts a retarding force on the rod, perfectly converting mechanical work into electrical heat.

This is energy conservation in action — Lenz’s law is just a way to state that you cannot get electrical energy for free.

Alternative Method

Use $\varepsilon = -d\Phi/dt$. Flux through the loop $= B \times (\text{area}) = B \times Lx$ where $x$ is the rod’s position. Then $d\Phi/dt = BL\, dx/dt = BLv$. Same emf.