Physics • Year 12 • Module 6 • Lesson 14
Lenz's Law and Direction
Apply Lenz's Law to real scenarios, interpret a flux-time graph, and evaluate the conservation of energy argument in electromagnetic induction contexts.
1. Classify and predict — magnet and loop scenarios
A bar magnet is manipulated near a circular loop of wire lying in the plane of the page. The table describes six scenarios. For each one, complete the missing cells using Lenz's Law and the right-hand grip rule. 12 marks (2 per row)
| Scenario | Direction of induced B field | Current direction (viewed from left) | Force on magnet |
|---|---|---|---|
| North pole moved toward loop from the left; flux through loop increasing to the right | Repulsion (opposes approach) | ||
| North pole pulled away from loop to the left; flux through loop decreasing | |||
| South pole moved toward loop from the left; flux increasing to the left | Points to the right (opposing leftward increase) | ||
| Bar magnet stationary, centred in loop | No force | ||
| Loop moved toward stationary north pole (same as N pole approaching) | |||
| Loop area decreased while kept perpendicular to a uniform field pointing right; flux decreasing | Clockwise (viewed from right) | N/A (no magnet) |
2. Interpret graph — flux vs time through a coil
The graph below shows the magnetic flux Φ through a single-turn coil as a function of time. Use it to answer the questions. 9 marks
Figure 2.1. Magnetic flux through a coil of resistance 2.0 Ω. Illustrative data. The external magnetic field points perpendicularly into the coil face throughout.
2.1 Identify the region(s) (A, B, C, D) in which an emf is induced in the coil. Justify your answer. 2 marks
2.2 Calculate the magnitude of the induced emf during Region A and during Region C. Show full working. 3 marks
2.3 Using Lenz's Law, state the direction of the induced current during Region A relative to the external field direction (same direction as external B, or opposite). Explain your reasoning. 2 marks
2.4 During Region C the flux is decreasing. State the direction of the induced current relative to Region A (same direction or reversed). Justify with Lenz's Law. 2 marks
3. Predict and justify — magnet falling through a copper tube
A bar magnet is dropped from rest through a long vertical copper tube. It takes noticeably longer to fall through than an identical non-magnetic rod of the same mass and dimensions. 8 marks
Context. Copper is not ferromagnetic — it is not attracted to a magnet in the conventional sense. Yet a magnet falls slowly through a copper tube. This is sometimes demonstrated as a “magnetic braking” effect.
3.1 As the magnet enters the top of the tube, explain what happens to the magnetic flux through a small ring-shaped section of the tube just above the magnet. Is the flux increasing or decreasing? 2 marks
3.2 Apply Lenz's Law to explain what direction of current is induced in that ring-section of tube, and what force this exerts on the falling magnet. 2 marks
3.3 Consider the ring-section of tube just below the magnet as it falls through. The flux through this lower section is now decreasing. What direction is the force on the magnet from this lower section? 2 marks
3.4 Explain, using conservation of energy, where the kinetic energy lost by the slower-falling magnet goes. 2 marks
4. Evaluate a student argument — aided vs opposed current
A student writes the following: “When a north pole approaches a loop, the induced current creates a field that attracts the magnet, making it move faster. This means we can get more electrical energy from the same magnet just by letting it run. Lenz's Law must be wrong because more energy would be generated.” 5 marks
4.1 Identify the specific error in the student’s claim about the direction of the force on the magnet. 1 mark
4.2 Explain what would actually happen — in terms of force, acceleration, and energy — if the induced current did aid the flux change instead of opposing it. Use a chain of reasoning with at least three steps. 3 marks
4.3 State the conservation law that is violated by the student’s scenario. 1 mark
Q1 — Classification table
Row 1 (N approaching, given: repulsion): Induced B = Points left (opposing rightward increase) • Current = Anticlockwise viewed from left.
Row 2 (N receding): Induced B = Points right (same as external B, reinforcing decreasing flux) • Current = Clockwise viewed from left • Force on magnet = Attraction (pulls magnet back).
Row 3 (S approaching, given: induced B points right): Current = Anticlockwise viewed from left (thumb points right, fingers curl anticlockwise from left side). Wait — right-hand grip: thumb right → fingers curl clockwise when viewed from left. Correction: Clockwise viewed from left • Force = Repels approaching south pole.
Row 4 (Stationary, given: no force): Induced B = None (zero) • Current = Zero.
Row 5 (Loop moves toward stationary N): Flux through loop increases to the right (same as N approaching) • Induced B = Points left (opposing) • Current = Anticlockwise viewed from left • Force on loop = Repulsion (loop is pushed back).
Row 6 (Loop area decreases in rightward field; current clockwise viewed from right, given): Flux decreasing (rightward) • Induced B = Points right (reinforcing decreasing flux) • Current clockwise viewed from right = anticlockwise viewed from left.
Marking note: Award 1 mark per correct cell. Accept logically consistent directions that follow from the student’s chosen reference frame as long as all four cells in a row are internally consistent.
Q2.1 — Regions with induced emf
Regions A and C. In Region A (0–1 s) flux increases at a constant rate, producing a constant induced emf. In Region C (3–5 s) flux decreases at a constant rate, producing a constant induced emf. In Region B (1–3 s) flux is constant (ΔΦ/Δt = 0), so no emf is induced. In Region D (5–6 s) flux is zero and constant — no emf.
Q2.2 — Magnitude of induced emf
Region A: ΔΦ = 4 − 0 = 4 mWb = 4 × 10−3 Wb; Δt = 1 s; N = 1. ϵ = N|ΔΦ/Δt| = 1 × (4 × 10−3)/1 = 4 × 10−3 V (4 mV). [1]
Region C: ΔΦ = 0 − 4 = −4 mWb; Δt = 2 s. ϵ = 1 × (4 × 10−3)/2 = 2 × 10−3 V (2 mV). [1]
Correct units and formula cited [1].
Q2.3 — Current direction Region A
During Region A the flux (pointing into the coil face) is increasing. By Lenz's Law the induced field must oppose this increase, so the induced B points out of the coil face (opposite to the external B). Using the right-hand grip rule with the thumb pointing out of the coil face, the current flows anticlockwise when viewed from the front (the side the external B enters). [1 — correct direction; 1 — correct Lenz's Law reasoning]
Q2.4 — Current direction Region C
During Region C the flux is decreasing. By Lenz's Law the induced field must now reinforce the decreasing flux, pointing into the coil face (same as external B). This requires the current to flow clockwise when viewed from the front — the opposite direction to Region A. [1 — reversed; 1 — Lenz reasoning]
Q3.1 — Flux in ring above magnet
As the magnet falls into the tube, the magnetic field from the magnet passes through the ring-section just above. As the magnet approaches and then passes, the flux through that upper ring first increases (magnet approaching) then decreases (magnet receding downward). As the magnet enters the tube, the flux through the section above is initially increasing. [1 — increasing; 1 — correct explanation]
Q3.2 — Current direction and force above magnet
Flux through the upper ring is increasing in the direction of the magnet’s field. By Lenz's Law, the induced current in that ring creates a field opposing the increase (opposing the magnet’s field). This means the ring behaves like a magnet with the same pole facing the approaching north pole, creating an upward (repulsive) force on the falling magnet — opposing its downward motion. [1 — direction; 1 — upward repulsive force]
Q3.3 — Force from ring below magnet
As the magnet moves below the lower ring, the flux through that ring is decreasing. By Lenz's Law, the induced current reinforces the decreasing flux, making the lower ring behave like a magnet attracting the one above it. This exerts an upward (attractive) force on the falling magnet, again opposing the downward motion. Both the upper and lower induced currents produce upward forces. [1 — upward; 1 — attraction reasoning]
Q3.4 — Conservation of energy
The kinetic energy “lost” by the slower-falling magnet is converted into electrical energy in the induced currents in the copper tube walls. Since copper has electrical resistance, these induced currents dissipate the electrical energy as heat (thermal energy) in the tube. Energy is conserved: gravitational potential energy → kinetic energy → electrical energy (induced currents) → thermal energy. No energy is destroyed. [1 — converted to electrical/heat; 1 — links to conservation of energy explicitly]
Q4.1 — Identifying the error
The student claims the induced current creates an attracting force. This is incorrect: by Lenz's Law, the induced current creates a field that repels the approaching north pole — opposing, not aiding, its approach.
Q4.2 — Chain of reasoning
(1) If the induced current aided the flux change, it would create a field attracting the approaching magnet. (2) The magnet would therefore accelerate toward the loop, increasing the rate of flux change. (3) A greater rate of flux change would induce a larger current, which would attract the magnet even more strongly, causing further acceleration. (4) The magnet would continue to accelerate indefinitely, generating ever-increasing electrical energy with no external energy input. This is a perpetual motion machine — impossible. [1 per clear step, max 3]
Q4.3 — Conservation law violated
The Law of Conservation of Energy (First Law of Thermodynamics) — energy cannot be created from nothing.