Two Sides of One Coin: Currents Make Fields, Changing Fields Make Currents
120 min · HS-PS2-5
Objective
Students will plan and conduct investigations to provide evidence that (1) an electric current produces a magnetic field around it, and (2) a changing magnetic flux through a coil induces an electric current, and will use this evidence to predict the direction and relative size of induced currents in a simple generator scenario.
Hook
8 minBring students in to a live induction-cooktop demonstration (or a 60-second clip if the cooktop is not available): a pot of water sits on a cold glass surface, yet within 30 seconds it is boiling. Nothing between the coil and the pot is hot — you can rest a paper towel on the glass next to the pot and it doesn't burn. Ask: 'The burner never gets hot. The glass never gets hot. So where is the energy coming from, and how does it get into the pot?' Take 3-4 student guesses on the board without judging. Then place a small neodymium magnet on the glass — it doesn't stick (glass is not magnetic). Reveal the punchline: underneath the glass is a coil of wire carrying a rapidly changing current. That changing current makes a changing magnetic field, which induces swirling currents in the steel pot, which heat the pot directly. Tell them: 'By the end of today you will have built the two halves of that cooktop yourselves — a current that makes a field, and a changing field that makes a current.'
Direct instruction
- 10m
Beat 1 — Moving charges make magnetic fields (Oersted & the right-hand rule)
Content
In 1820 Hans Christian Ørsted noticed that a compass needle deflected whenever he switched on a nearby current. That single observation linked electricity and magnetism forever: an electric current — moving charges — produces a magnetic field in the space around it. The field is NOT stored in the metal; turn the current off and the field vanishes instantly. For a long straight wire the magnetic field lines form concentric circles around the wire, and their direction is given by the right-hand rule: point the right thumb along the conventional current, and the fingers curl in the direction of B. The magnitude falls off with distance: B = μ₀I/(2πr), so doubling the current doubles the field, and doubling the distance from the wire halves it. Worked example: a wire carries I = 5.0 A; at r = 2.0 cm = 0.020 m the field magnitude is B = (4π × 10⁻⁷ T·m/A)(5.0 A)/(2π × 0.020 m) = 5.0 × 10⁻⁵ T — roughly Earth's field, which is exactly why Ørsted's compass moved.
Delivery
Emphasize the phrase 'moving charges make magnetic fields' — repeat it three times, because the misconception you are killing is 'the field lives in the metal.' Ask: 'If I cut the battery, what happens to the compass needle?' (It snaps back to north — the field is gone.) Have every student physically make the right-hand rule with their own hand while you talk through the concentric-circle diagram on the slide. Check for the classic error of using the LEFT hand or curling the thumb — walk the room and correct grips. Close by tying the calculated 5 × 10⁻⁵ T back to the hook: this is why Ørsted, holding a compass over a battery wire, saw the needle twitch — and why students in Lab Station A will see the same twitch in five minutes.
- 10m
Beat 2 — From a straight wire to a solenoid: building an electromagnet
Content
One loop of current-carrying wire concentrates the field through the middle of the loop (use the right-hand rule on each side of the loop and the fields add through the center). Stack many loops in a tight coil — a solenoid — and the interior field becomes strong and nearly uniform, while the field outside looks just like a bar magnet, with a north end (where field lines exit) and a south end (where they enter). Inside an ideal solenoid B = μ₀nI, where n is turns per meter. Two knobs control the strength: current I and turn density n. Wrapping the coil around a soft-iron core (a nail) multiplies the field by hundreds because the iron's own domains align with the coil's field — this is why a nail-and-battery electromagnet can pick up paperclips, and why real electromagnets in junkyards use iron cores. Worked prediction: if 20 turns of wire on a nail with 1.0 A lifts 4 paperclips, then doubling to 40 turns at the same current should roughly double the lift to ~8, and doubling the current to 2.0 A on top of that should roughly double again to ~16 (in practice you'll saturate the iron before then — good talking point).
Delivery
Connect straight-wire field lines to loop field lines by asking, 'If the wire curls, where do the field circles pile up?' — students should see they add through the loop's center. Introduce n = turns/length as a design variable students will control in Lab A. Pre-empt the misconception 'the nail is the magnet': ask 'What happens to the paperclips when I disconnect the battery?' They fall. The iron is a field-amplifier, not the source. Set the expectation that in Lab Station A they'll test the linear I-vs-lift and n-vs-lift predictions and should get roughly proportional trends until saturation.
- 12m
Beat 3 — Faraday's law: a CHANGING flux induces a current
Content
The reverse effect, discovered by Faraday in 1831: if the magnetic flux Φ through a loop changes with time, an EMF is induced in the loop. Faraday's law: EMF = −ΔΦ/Δt, where Φ = B·A·cos(θ). Three ways to change Φ: change B (move a magnet closer/farther, or change the current in a nearby coil), change A (stretch or shrink the loop), or change θ (rotate the loop — this is exactly what a generator does). The crucial word is CHANGING. A magnet held motionless inside a coil produces zero induced current, even though the field through the coil is huge. Only the CHANGE matters, and the FASTER the change, the LARGER the EMF. Lenz's law fixes the sign: the induced current flows in the direction whose own magnetic field opposes the change in flux — nature resists the change. Worked example: a coil has 200 turns and area 5.0 × 10⁻³ m². The field through it drops from 0.40 T to 0 in 0.10 s. ΔΦ per turn = (0 − 0.40)(5.0 × 10⁻³) = −2.0 × 10⁻³ Wb. Total EMF magnitude = N·|ΔΦ/Δt| = 200 × (2.0 × 10⁻³ / 0.10) = 4.0 V. If instead the field dropped in 0.010 s, the EMF would be 40 V — ten times the change rate, ten times the voltage.
Delivery
Say the phrase 'a changing field induces a current' and have students repeat it. Then do the mini-thought experiment out loud: 'Magnet sitting still deep inside a coil — needle reads what?' (Zero.) 'Now I yank it out fast — needle reads what?' (A brief spike.) 'Now I yank it out twice as fast — needle reads what?' (A bigger spike.) This directly attacks the misconception that 'faster just means the current arrives sooner' — no, faster means BIGGER. Walk through the numerical example on the slide slowly; the factor-of-ten jump from 4.0 V to 40 V is the punchline. Introduce Lenz's law as 'nature pushes back' — students will see the sign flip when they reverse the magnet's motion in Lab Station B.
- 5m
Beat 4 — Putting it together: the AC generator
Content
A generator is the mechanical inverse of a motor. A coil of N turns and area A is rotated at angular speed ω between the poles of a permanent magnet. As the loop rotates, the angle θ between B and the loop's normal changes continuously: θ = ωt. The flux through one turn is Φ = BA·cos(ωt), and Faraday's law gives EMF = NBAω·sin(ωt) — a sinusoidal alternating voltage with peak value NBAω. Every knob you can turn on that expression is a design lever: more turns N, stronger magnet B, bigger loop A, or spin it faster ω, all raise the peak voltage. This is where hydro, wind, and nuclear plants all end: something spins a coil in a magnetic field. Slip rings carry the alternating current out to the load.
Delivery
Tie every symbol in EMF = NBAω·sin(ωt) back to something students can point to on the generator diagram on the slide — 'this is N,' 'this is A,' 'this is ω.' Ask: 'If a wind turbine spins twice as fast in a storm, what happens to the peak voltage?' (Doubles.) Then ask the bridge question: 'A dam, a wind turbine, a nuclear plant — what physical thing do they all do at the end?' (Spin a coil in a magnetic field.) This sets up Activity 2, where they'll drive a hand-cranked generator and measure exactly this.
Activities
- 30m
Lab Station A — Oersted's experiment + electromagnet design testLab
Students work in groups of 3. Distribute the handout below and the materials. Groups rotate through Part 1 (Oersted) in the first 8 minutes, then move to Part 2 (electromagnet design) for the remaining 22 minutes. Circulate to check right-hand-rule predictions and to confirm the circuit is broken (switch open) whenever they're rewinding the nail — a shorted D-cell gets hot fast. Student handout — Lab A: Currents Make Fields Part 1 — Oersted's compass (8 minutes) - Lay a straight ~30 cm segment of wire flat on the table, oriented North-South, and place the compass directly UNDER the wire. Let the needle settle. - Compass needle direction with no current: ______ - Connect the wire ends to the battery through the switch. Close the switch for ~2 seconds ONLY. - Compass needle direction with current flowing: ______ - Estimate the deflection angle from North: ______ ° - Reverse the battery leads and repeat. - New deflection direction: ______ - Using the right-hand rule, predict which way the field points UNDER the wire when current flows from South to North through it, and check against your compass reading. - Prediction: ______ - Observation matches prediction? Y / N - The switch stays OPEN except during a reading. A closed circuit with no resistance drains and heats the D-cell. Part 2 — Electromagnet design test (22 minutes) Build a nail electromagnet: wrap insulated wire tightly around the nail, leaving ~15 cm of lead on each end. Strip the ends. Connect through the ammeter and switch to the D-cell. When the switch is closed, dip the nail head into the pile of paperclips and lift straight up. Count clips that stay attached after 3 seconds. - Trial 1: 20 turns, one D-cell (~1.5 V) - Measured current I = ______ A - Paperclips lifted = ______ - Trial 2: 40 turns, one D-cell - Measured current I = ______ A - Paperclips lifted = ______ - Trial 3: 40 turns, TWO D-cells in series (~3 V) - Measured current I = ______ A - Paperclips lifted = ______ - Trial 4 (control): 40 turns, switch OPEN (no current) - Paperclips lifted = ______ Analysis questions (answer in complete sentences below the table): 1. From Trial 1 → Trial 2, what did you change and what happened to the lift? What does that tell you about turn density n? 2. From Trial 2 → Trial 3, what did you change and what happened? What does that tell you about current I? 3. Trial 4 is a control. What claim does it let you rule out? (Hint: 'The magnetism comes from the ______.') 4. Predict: if you tripled the turns AND doubled the current, would the lift be 6× the Trial 1 value? Why might the real answer be less? (Look up 'magnetic saturation.')
Materials
- Compass (1 per group)
- Insulated 22-gauge copper wire, ~1 m per group
- D-cell battery with holder (1 per group)
- Knife switch or simple pushbutton
- Iron nail, 8-10 cm (1 per group)
- Box of small steel paperclips (~50 per group)
- Ruler
- Ammeter or multimeter set to DC current (0-3 A)
Example outputs
- Part 1: With no current the needle points North. With current flowing S→N through the wire, the needle under the wire deflects ~40° to the West. Reversing the battery flips the deflection to the East. Right-hand rule prediction (thumb S→N, fingers curl): field points West under the wire — matches.
- Part 2: Trial 1 (20 turns, 1.5 V) → I ≈ 1.2 A, lifts 3 clips. Trial 2 (40 turns) → I ≈ 1.1 A, lifts 7 clips. Trial 3 (40 turns, 3 V) → I ≈ 2.2 A, lifts 13 clips. Trial 4 (no current) → 0 clips. Conclusion: doubling n roughly doubled the lift; doubling I roughly doubled the lift again; with no current the nail lifts nothing, so the field comes from the current, not the iron.
- 40m
Lab Station B — Induction with coil + magnet + galvanometer, and PhET generatorLab
Groups of 3 continue at Station B. This is the induction half of the lesson: they FIRST use real hardware (coil + magnet + galvanometer) to see that only MOTION produces a reading, and that faster motion produces a bigger reading. THEN they open the PhET Faraday's Electromagnetic Lab simulation to test the generator model quantitatively. Handout below is theirs to fill in. PhET URL (open the 'Generator' and 'Pickup Coil' tabs): https://phet.colorado.edu/en/simulations/faradays-law and https://phet.colorado.edu/en/simulations/faradays-electromagnetic-lab Student handout — Lab B: Changing Fields Make Currents Part 1 — Real coil and magnet (15 minutes) Connect the coil to the galvanometer with alligator leads. Zero the needle. - Test 1: Hold the magnet motionless INSIDE the coil for 5 seconds. - Galvanometer reading: ______ - Test 2: Push the N pole of the magnet INTO the coil at moderate speed. - Needle deflects LEFT / RIGHT (circle one), size: small / medium / large - Test 3: Pull the same N pole OUT of the coil at moderate speed. - Needle deflects LEFT / RIGHT, size: small / medium / large - Test 4: Push the N pole IN, this time as fast as you can. - Needle deflects LEFT / RIGHT, size: small / medium / large - Test 5: Flip the magnet. Push the S pole IN at moderate speed. - Needle deflects LEFT / RIGHT, size: small / medium / large Claim-Evidence-Reasoning box: - Claim: A ______ magnetic field induces a current; a ______ magnetic field does not. - Evidence: (cite Test numbers) ______ - Reasoning: Using Faraday's law EMF = −ΔΦ/Δt, explain in 2-3 sentences why Test 1 gave zero and Test 4 gave the biggest deflection. Part 2 — PhET Faraday's Electromagnetic Lab, 'Pickup Coil' tab (12 minutes) Open the simulation. Drag the bar magnet through the pickup coil at three different speeds and record the peak bulb brightness (or peak voltmeter reading if enabled). - Slow drag: peak reading = ______ - Medium drag: peak reading = ______ - Fast drag: peak reading = ______ - Now increase the coil from 1 loop to 3 loops. Repeat medium drag. - 1 loop: ______ 3 loops: ______ - Move the magnet so it sits still INSIDE the coil. - Reading = ______ Part 3 — PhET 'Generator' tab (13 minutes) Open the Generator tab. A water wheel spins a bar magnet inside a pickup coil. - Set the water flow to LOW. Peak voltmeter reading: ______ V - Set the water flow to HIGH. Peak voltmeter reading: ______ V - Ratio (High / Low) of readings: ______ - Ratio of rotation rates (High / Low, from RPM display): ______ - Are the two ratios approximately equal? Y / N. Explain using EMF = NBAω·sin(ωt). - Now increase the number of pickup-coil loops from 2 to 4. Predict what happens to the peak voltage, then test. - Prediction: ______ - Observed change: ______ Wrap-up question: In one paragraph, explain to a friend how a hydroelectric dam turns falling water into electricity in your kitchen — use the words flux, coil, changing, and induced.
Materials
- 200-turn coil (or hand-wound 100+ turn coil on a cardboard tube)
- Strong bar magnet or neodymium magnet
- Analog galvanometer (center-zero, sensitive) or multimeter on µA setting
- Alligator-clip leads
- Chromebook/laptop for PhET (1 per group)
- Stopwatch or phone timer
Example outputs
- Part 1: Test 1 (still magnet) — needle reads 0. Test 2 (N pole in, medium) — deflects right, medium. Test 3 (N pole out, medium) — deflects LEFT, medium (opposite direction, same size). Test 4 (N pole in, fast) — deflects right, LARGE. Test 5 (S pole in) — deflects LEFT. Claim: a CHANGING field induces current; a STEADY field does not. Reasoning: Test 1 has ΔΦ/Δt = 0 so EMF = 0. Test 4 shrinks Δt, so |ΔΦ/Δt| is much larger, so the induced EMF and current are much larger.
- Part 3: Low flow ~2.0 V peak at ~15 RPM; High flow ~6.0 V peak at ~45 RPM. Both ratios ≈ 3, matching EMF ∝ ω. Doubling loops from 2 to 4 roughly doubles the peak voltage, matching EMF ∝ N. Wrap-up: falling water spins a turbine, which spins a magnet inside a coil. The flux through the coil changes as the magnet rotates, so an EMF is induced in the coil — that induced current is the electricity that reaches the kitchen outlet.
Formative assessment
15 minA student holds a strong bar magnet completely still, deep inside a 500-turn coil connected to a sensitive galvanometer. The galvanometer reads zero. The student concludes: 'This magnet must be broken — a strong magnet inside a coil should push a big current.' Explain, using Faraday's law, why the student is wrong. What would they need to do to get a nonzero reading?
short answerThe magnet is not broken. Faraday's law says EMF = −N·ΔΦ/Δt — the induced EMF depends on the RATE OF CHANGE of flux, not on the flux itself. A motionless magnet gives ΔΦ/Δt = 0, so the induced EMF is 0 and no current flows, no matter how strong the magnet is. To get a reading the student must change the flux: move the magnet in or out, rotate it, or change the coil's shape. The faster the change, the larger the induced current.A single-loop generator with area A = 0.020 m² spins at angular speed ω = 60 rad/s between the poles of a magnet with B = 0.50 T. (a) Write the expression for the peak EMF. (b) Calculate the peak EMF. (c) If an engineer doubles the number of turns to N = 2 AND triples the angular speed, by what factor does the peak EMF change?
calculation(a) Peak EMF = NBAω. (b) With N = 1: Peak EMF = (1)(0.50 T)(0.020 m²)(60 rad/s) = 0.60 V. (c) N goes from 1 to 2 (×2) and ω triples (×3), so peak EMF changes by a factor of 2 × 3 = 6. New peak EMF = 6 × 0.60 V = 3.6 V.You wrap 30 turns of wire around an iron nail and connect it briefly to a D-cell. The nail picks up 5 paperclips. Which single change would MOST INCREASE the number of paperclips the electromagnet can lift?
multiple choiceCorrect answer: B. Replace the D-cell with a fresh 9 V battery (larger current I, which raises B = μ₀nI proportionally). A) Removing the iron nail REDUCES the field (iron amplifies it). C) Cutting the wire OPENS the circuit, killing the current, so lift → 0. D) Holding the nail still does nothing — the field comes from the current, not from motion. Options given to the student: A) Remove the iron nail. B) Replace the D-cell with a fresh 9 V battery. C) Cut the wire in half. D) Hold the nail perfectly still while lifting.Design an investigation to test the claim: 'The direction of the induced current in a coil depends on which pole of the magnet is moving and on whether it is moving toward or away from the coil.' Describe your independent variable, dependent variable, at least one controlled variable, and the minimum four trials you would run.
short answerIndependent variable: the combination of magnet pole (N or S) and direction of motion (in or out). Dependent variable: direction of galvanometer needle deflection (left or right). Controlled variables: speed of magnet motion, number of turns in the coil, distance the magnet travels, same coil and same magnet each trial. Minimum four trials: (1) N pole pushed IN, (2) N pole pulled OUT, (3) S pole pushed IN, (4) S pole pulled OUT. Expected result: Trials 1 and 4 deflect the needle one way; Trials 2 and 3 deflect it the other way. This shows the induced current reverses when EITHER the pole is flipped OR the direction of motion is reversed, supporting Lenz's law.
Vocabulary
- electric current
- The flow of electric charge through a conductor, measured in amperes (A). A steady current is a continuous flow of moving charges.
- magnetic field
- A vector field, symbol B, measured in tesla (T), that exerts a force on moving charges and magnetic materials. Produced by moving charges.
- electromagnet
- A coil of current-carrying wire (often wrapped around an iron core) that behaves as a magnet only while current flows.
- solenoid
- A long, tightly wound coil of wire. When current flows, the field inside is nearly uniform and the outside field looks like a bar magnet's.
- right-hand rule
- For a straight wire: point the thumb in the direction of conventional current; the fingers curl in the direction of the magnetic field lines.
- magnetic flux
- Φ = B·A·cos(θ), the amount of magnetic field passing through a loop of area A. Measured in webers (Wb).
- electromagnetic induction
- The production of an EMF (voltage) and induced current in a conductor when the magnetic flux through it changes.
- Faraday's law
- The induced EMF equals the negative rate of change of magnetic flux: EMF = −ΔΦ/Δt. Faster flux change → larger induced voltage.
- induced current
- Current driven by an induced EMF; its direction opposes the change in flux (Lenz's law).
- generator
- A device that rotates a coil in a magnetic field so that flux changes continuously, producing an alternating induced current.
Common misconceptions
- 'A stationary magnet inside a coil pushes a current because the field is strong.' No — Faraday's law depends on ΔΦ/Δt, not Φ. A stationary magnet gives ΔΦ/Δt = 0 and induces zero current, no matter how strong the field. Lab B Test 1 makes this vivid.
- 'The magnetic field is stored in the metal of the wire (or nail).' No — the field is produced by the moving charges. Trial 4 in Lab A is the direct test: same coil, same nail, switch open → zero lift. The moment current stops, the field is gone.
- 'Electricity and magnetism are separate topics that just happen to interact.' No — they are two aspects of one electromagnetic interaction. Moving charges make magnetic fields (Beat 1), and changing magnetic fields make currents in charges (Beat 3). Ørsted and Faraday together closed the loop.
- 'Spinning a generator faster just makes the current arrive sooner — the peak size is the same.' No — Faraday's law says peak EMF = NBAω, so peak voltage scales linearly with ω. Twice the rotation rate is twice the peak voltage, not the same voltage sooner. Lab B Part 3 lets students measure this ratio.
- 'The right-hand rule works for any direction of current.' Students often forget it applies to CONVENTIONAL current (positive charge flow). If a problem gives electron flow, they must reverse the direction first, then apply the right hand.
Materials checklist
- Compasses (1 per group of 3)
- Insulated 22-gauge copper wire (~1.5 m per group)
- D-cell batteries with holders (2 per group)
- Iron nails, 8-10 cm (1 per group)
- Small steel paperclips (~50 per group)
- Multimeter or ammeter, 0-3 A DC (1 per group)
- 200-turn coils on tubes (1 per group; or materials to hand-wind)
- Strong bar magnets or neodymium magnets (1 per group)
- Center-zero galvanometers, or multimeters with µA setting (1 per group)
- Alligator-clip lead sets
- Chromebooks/laptops with internet access (1 per group)
- Stopwatches or phone timers
- Printed Lab A handout (1 per student)
- Printed Lab B handout (1 per student)
- Push-button switches or knife switches (1 per group)