Motional EMFJEE Main

Concept

Move a conducting rod across a magnetic field and it becomes a battery. The changing area of the circuit changes the magnetic flux, which by Faraday's law induces an EMF. Lenz's law says the induced current opposes the motion — so you must keep pushing.

Key formula

Derivation

Flux through the circuit is $\Phi = B\,L x$, where $x$ is the rod's position. Faraday's law: $\varepsilon = -\dfrac{d\Phi}{dt} = -BL\dfrac{dx}{dt} = -BLv$, magnitude $BLv$.

The current $I = \varepsilon/R$ flows through the rod, which sits in field $B$, so it feels a force $F = BIL = B^2L^2v/R$ directed against its motion (Lenz's law). The power you supply, $Fv$, equals the electrical power $I^2R$.

Scenarios to explore

• Motional EMF — A rod sliding through a field — Faraday & Lenz.

Real-world applications

• Electric generators (rotating coils instead of sliding rods).
• Eddy-current braking in trains and treadmills.
• Induction cooktops and electromagnetic flow meters.

JEE exam tips

• Terminal velocity of a falling rod: set $mg = B^2L^2v/R$ and solve for $v$.
• Energy check: mechanical power $Fv$ in = electrical power $I^2R$ out.

Common mistakes

• Dropping the minus sign / Lenz direction — the force always opposes motion.
• Confusing the retarding force $B^2L^2v/R$ with the motional EMF.
• Forgetting EMF needs a change in flux — a stationary rod gives nothing.

Exam traps to avoid

• Only the component of velocity perpendicular to both $B$ and the rod produces EMF.
• If the circuit is open ($R\to\infty$), EMF still exists but no current flows and no force acts.