A conducting rod of length 0.4 m moves perpendicular to a uniform magnetic field of 3 T at a speed of 5 m/s. What EMF is induced across the rod?
A0.27 V, calculated as B/(L·v)
B6 V, calculated as B·(L + v)
C6 V, calculated as B·L·v = 3 × 0.4 × 5
D15 V, calculated as B·v/L
ε = BLv = 3 × 0.4 × 5 = 6 V. The formula comes from two equivalent derivations: the Lorentz force on charge carriers (F = qvB along the rod, giving work per unit charge = BLv over length L), and Faraday's law (the rod sweeps area dA = L·v·dt per unit time, so dΦ/dt = B·L·v). Both give the same result. The other options all use wrong arithmetic operations — the formula is strictly a product of the three quantities.
Question 2 Multiple Choice
What is the microscopic physical origin of motional EMF when a conductor moves through a magnetic field?
AThe motion induces a changing magnetic field inside the conductor, which in turn creates an electric field by Faraday's law
BThe conductor's free electrons experience the Lorentz force F = qv × B as they move with the conductor, separating charges and creating a potential difference
CThe external magnetic field does work directly on the conductor's lattice, which transfers energy to the free electrons
DThe conductor's motion creates a gravitational gradient that separates charge by density
At the microscopic level, free charge carriers in the moving conductor are themselves moving with it (velocity v). Each carrier feels the Lorentz force F = q(v × B), which pushes positive charges to one end and negative charges to the other. This charge separation builds up until the resulting electric field exactly balances the magnetic force — at that point, the potential difference across the rod equals the work done by the magnetic force per unit charge, which integrates to BLv. This is the physical mechanism that Faraday's law encodes at the macroscopic level.
Question 3 True / False
The motional EMF formula ε = BLv can be derived both from the Lorentz force on moving charges and from Faraday's law applied to the changing loop area — and both derivations give the same answer.
TTrue
FFalse
Answer: True
These are two equivalent descriptions of the same physics, not two different effects. The Lorentz force approach tracks what happens to individual charge carriers (F = qv × B, integrated over the rod length gives ε = BLv). The Faraday's law approach tracks the circuit as a whole (the moving rod sweeps area dA = L·v·dt, so dΦ/dt = B·L·v = ε). The agreement is fundamental: Faraday's law, at its core, is a statement about the Lorentz forces on charges when either the field or the conductor changes.
Question 4 True / False
In an electromagnetic generator, the coil produces a constant (DC) voltage because the magnetic field is uniform and steady throughout the rotation.
TTrue
FFalse
Answer: False
Even in a uniform steady magnetic field, a rotating coil produces sinusoidal AC voltage. The flux through the coil is Φ = BA cos(ωt) — it varies sinusoidally because the angle between the field and the area vector changes continuously as the coil rotates. By Faraday's law, ε = −dΦ/dt = BAω sin(ωt), which is AC. The field being uniform and steady does not prevent AC generation; the rotation itself creates the sinusoidally changing flux. Every power plant on Earth produces AC for this reason.
Question 5 Short Answer
Two students disagree about the origin of motional EMF. One says it comes from changing magnetic flux (Faraday's law). The other says it comes from the Lorentz force on moving charges. Who is right?
Think about your answer, then reveal below.
Model answer: Both are right — they are describing the same physical phenomenon from two complementary perspectives. The Lorentz force (F = qv × B) is the microscopic mechanism: charge carriers moving with the rod feel a force that separates them, creating a potential difference. Faraday's law is the macroscopic description: the moving rod sweeps out new loop area, increasing the flux, and the induced EMF equals the rate of flux change. Both give ε = BLv. Neither is more fundamental — they are equivalent formulations of the same underlying electromagnetism.
This equivalence is not coincidental — it reflects the deep unity of Maxwell's equations. Faraday's law in integral form captures the collective result of Lorentz forces on all the charge carriers in the conductor. When you compute dΦ/dt for a moving conductor in a steady field, you're implicitly summing the work done by v × B forces along the rod's length. The two perspectives are connected by the mathematics of flux through a moving surface, and their agreement is a consistency check on Maxwell's theory.