Electromagnetic Induction: Speed-Solving Techniques (6)

Question

A rod of length $L = 0.5\ \text{m}$ moves with velocity $v = 4\ \text{m/s}$ perpendicular to a uniform magnetic field $B = 0.2\ \text{T}$. Find the EMF induced. Solve in 10 seconds.

Solution — Step by Step

Final answer: $\varepsilon = 0.4\ \text{V}$.

Why This Works

The $BLv$ formula is the special case of Faraday’s law where the geometry is clean: straight rod, uniform $B$, perpendicular motion. JEE and NEET love this setup because it reduces to a one-line product.

The deeper reason: in time $dt$, the rod sweeps area $L \cdot v\, dt$, so flux change is $B \cdot L \cdot v\, dt$, and EMF is $d\Phi/dt = BLv$.

Alternative Method

Use the Lorentz force on charges: each free electron in the rod experiences $F = qvB$, equivalent to an electric field $E = vB$ along the rod. Multiplying by length gives $\varepsilon = vBL$. Same answer, slightly more physical.

Common Mistake