Questions: Lenz's Law and Direction of Induced Currents

Question 1

A bar magnet with its north pole pointing downward is pulled away from (below) a horizontal conducting loop. The downward magnetic flux through the loop is therefore decreasing. What does Lenz's law predict about the induced current?

• A. The induced current flows counterclockwise (viewed from above), creating an upward field to oppose the downward flux
• B. The induced current flows clockwise (viewed from above), creating a downward field to resist the decrease in downward flux
• C. No current is induced because the magnet is moving away, not toward the loop
• D. The induced current flows counterclockwise to repel the magnet and speed its departure

Answer: (B)

Lenz's law says the induced current opposes the *change* in flux, not the flux itself. The flux is downward and decreasing, so the induced current must try to maintain that flux by creating a magnetic field pointing downward. By the right-hand rule, a clockwise current (when viewed from above) produces a magnetic field pointing downward through the loop. This also creates an attractive force on the retreating magnet — you must do work to pull the magnet away, consistent with energy conservation. Option A describes opposing the flux itself (not the change), which is the classic misconception.

Question 2

Eddy current braking in trains works by passing conducting wheels through a magnetic field. What provides the braking force?

• A. The magnetic field directly attracts the iron in the wheels, slowing them
• B. Eddy currents induced in the moving conductor create magnetic forces that oppose the motion causing them
• C. The braking force comes from friction between the magnetic field lines and the wheel surface
• D. The induced EMF drives current into a resistor, heating it, and the wheel cools and contracts

Answer: (B)

As the conducting wheel moves through the magnetic field, the flux through different regions of the wheel changes, inducing closed loops of current (eddy currents) within the metal. By Lenz's law, these currents flow in directions that oppose the change in flux — which means they create forces opposing the wheel's motion. The kinetic energy of the wheel is converted to electrical energy (and then heat) in the conductor. No mechanical friction is involved in the braking itself.

Question 3

If a permanent magnet is held stationary inside a coil, a steady induced current flows in the coil as long as the magnet remains inside.

• T. True
• F. False

Answer: False

Faraday's law states EMF = −dΦ/dt: it is the *rate of change* of flux that drives the EMF, not the flux itself. A stationary magnet produces constant flux through the coil, so dΦ/dt = 0, and no EMF — and therefore no current — is induced. Current flows only while the flux is changing. This is a crucial distinction: the presence of a magnetic field does not induce current; only a *changing* magnetic field does.

Question 4

Lenz's law is a consequence of conservation of energy: if induced currents aided the change in flux rather than opposing it, energy would be created from nothing.

• T. True
• F. False

Answer: True

Imagine if induced currents aided the increase in flux: an approaching magnet would attract the loop, accelerating toward it, increasing the flux, inducing more current, creating more attraction — a runaway chain that produces energy from nothing. The fact that induced currents always oppose the change prevents this. The opposing force means you must do work to maintain the change (e.g., push a magnet toward a loop), and that work is exactly the electrical energy deposited in the circuit. Lenz's law is energy conservation applied to electromagnetic induction.

Question 5

A conducting ring is dropped from rest and falls through a region of uniform, horizontal magnetic field (entering from above, exiting below). Describe how the induced current and the ring's acceleration change as it enters, passes fully through, and exits the field region.

Model answer: Entering: flux through the ring increases, so an induced current flows to oppose the increase. This creates an upward magnetic braking force, so the ring accelerates more slowly than free fall. Fully inside: the flux is constant (uniform field, ring fully enclosed), so no current is induced and no braking force acts — the ring accelerates at g. Exiting: flux decreases, inducing a current that tries to maintain the flux, again producing an upward braking force and slowing the acceleration below g.

The key is tracking what is changing. Only the rate of change of flux matters, not the flux itself. When the ring is partially in or out of the field, flux changes and braking occurs. When fully inside a uniform field, flux is constant and the ring is in free fall. This three-phase behavior is a direct application of Lenz's law and explains why a superconducting ring would fall at constant velocity (infinite resistance → perfect Lenz braking) or no braking at all depending on the scenario.