Electromagnetic Induction
Michael Faraday, Royal Institution, London, 29 August 1831: Faraday wound two separate coils of wire around opposite sides of an iron ring. When he connected one coil to a battery, a galvanometer on the second coil twitched momentarily, then settled back to zero, even though a steady current kept flowing in the first coil. The needle only moved again when he broke the circuit. The key was change: $\text{EMF} = -N\dfrac{\Delta\Phi}{\Delta t}$. A steady field, however strong, induces nothing.
Three quick questions from earlier lessons. Pulling old material back to mind before you learn something new makes the new material stick better, so this is not busywork.
A bar magnet is held stationary inside a coil of wire connected to a galvanometer.
Predict 1: Does the galvanometer show a deflection while the magnet sits stationary inside the coil?
Predict 2: If the magnet is then pulled out of the coil quickly, how does the galvanometer reading compare with pulling it out slowly?
Electromagnetic induction requires:
Know
- Faraday's Law: $\text{EMF} = -N\dfrac{\Delta\Phi}{\Delta t}$
- Lenz's Law: induced current opposes the change in flux that produced it
- Eddy currents, generators and transformers ($V_s/V_p = N_s/N_p$)
Understand
- Why induction requires a changing flux, not just the presence of a field
- Why induced current opposes the change producing it (conservation of energy)
- Why slotted plates reduce eddy-current damping compared with solid plates
Can Do
- Predict the direction of an induced current using Lenz's Law
- Explain the operation of a generator and a transformer
- Explain eddy-current applications, such as induction cooktops, damping and wireless charging
Core Content
Wind two separate coils around opposite sides of an iron ring. Connect a galvanometer to one coil and a battery to the other. Close the switch, and the galvanometer needle jumps, but only for an instant, then settles back to zero, even though the battery keeps a steady current flowing. Open the switch, and the needle jumps again, in the opposite direction. This is what Michael Faraday observed at the Royal Institution on 29 August 1831. The needle only ever moved while the flux through the ring was changing, not while current was merely present. This single observation is the foundation of electromagnetic induction.
$\text{EMF} = -N\dfrac{\Delta\Phi}{\Delta t}$
$N$: number of turns; $\Delta\Phi$: change in magnetic flux (Wb); $\Delta t$: time interval (s). The negative sign encodes Lenz's Law, the direction of the induced EMF opposes the change producing it.
The induced current always flows in the direction that opposes the change in flux that produced it, never the direction that would reinforce it.
This is a direct consequence of conservation of energy: if the induced current reinforced the change instead, it would create energy from nothing.
A bar magnet, north pole down, is dropped through a horizontal copper ring. Explain why it falls slower than free fall.
- As the magnet approaches the ring, the flux through the ring (from the magnet's field) increases.
- By Lenz's Law, the induced current creates a field that opposes this increase, so the ring's near face behaves like the same pole as the approaching magnet.
- Like poles repel: this upward magnetic force partly opposes gravity, reducing the magnet's net downward acceleration.
- No energy is created: the induced current dissipates as heat ($I^2R$) in the ring, drawn from the magnet's kinetic and potential energy, consistent with conservation of energy.
Faraday's Law: $\text{EMF} = -N\Delta\Phi/\Delta t$, induced EMF is proportional to the rate of change of flux, not the flux itself. Lenz's Law: the induced current always opposes the change in flux that produced it, a consequence of conservation of energy. This is why a magnet dropped through a copper ring falls slower than free fall.
Pause, copy the highlighted formula and both laws into your book before the check below.
A stationary magnet inside a stationary coil induces no EMF, because the flux through the coil is not changing.
Faraday's Law states that the induced EMF is proportional to the size of the magnetic flux, not its rate of change.
Faraday's Law does not only apply to neat coils of wire, it applies to any conductor in a changing field, including a single solid block of metal. When a bulk conductor experiences a changing flux, circulating currents called eddy currents form within it, obeying Lenz's Law just like current in a coil. These currents dissipate energy as heat inside the conductor itself, sometimes a useful effect (induction cooktops), sometimes an unwanted energy loss engineers must design around (transformer cores).
A solid copper plate swung on a pendulum through a magnetic field slows down quickly, large eddy currents form and dissipate energy rapidly as heat.
Replace the solid plate with a slotted plate, and the pendulum swings for much longer, the slots break up the circulating current paths, reducing the eddy currents and the energy they dissipate.
$\dfrac{V_s}{V_p} = \dfrac{N_s}{N_p}$
$V_s$, $V_p$: secondary and primary voltage; $N_s$, $N_p$: secondary and primary turns. A changing current in the primary coil produces a changing flux, which induces an EMF in the secondary coil.
Generator: converts mechanical energy (rotation) into electrical energy by rotating a coil within a magnetic field, continuously changing the flux through the coil and inducing an alternating EMF.
Wireless phone charging: an AC current in the charging pad's coil creates a continuously changing magnetic field. This changing field induces a current in the phone's receiver coil, transferring energy without any physical contact.
Moving a magnet slowly into a coil produces a smaller $\Delta\Phi/\Delta t$, a smaller EMF, and a smaller galvanometer deflection.
Moving it quickly produces the same direction of deflection, but a much larger magnitude, since EMF depends on the rate of change, not the total flux change.
Eddy currents are circulating currents induced within a bulk conductor by a changing flux; they dissipate energy as heat, and slotting or laminating a conductor reduces this effect. A generator converts mechanical energy to electrical energy via induction; a transformer changes voltage according to $V_s/V_p = N_s/N_p$; wireless charging induces current in a receiver coil via a changing field from the charging pad.
Add eddy currents, the transformer ratio, and generator/wireless-charging applications to your notes before the check below.
A solid copper plate swinging on a pendulum through a magnetic field stops quickly. Replacing it with a slotted plate makes it swing for longer because:
- A bar magnet's north pole approaches a coil from above. Using Lenz's Law, describe the direction of the induced current in the coil (as viewed from above) and explain your reasoning.
- Explain why, once the magnet is held stationary inside the coil, the induced current drops to zero.
- Predict what happens to the induced current's direction when the same magnet is instead withdrawn from the coil.
Three of these are correct statements about electromagnetic induction. Pick the odd one out.
- A transformer has 200 turns on its primary coil and 1000 turns on its secondary coil. If the primary voltage is 240 V, calculate the secondary voltage.
- Explain, using Faraday's Law, why a transformer only works with alternating current (AC) and not direct current (DC).
- Describe how a wireless phone charger transfers energy to a phone using electromagnetic induction, referring specifically to changing magnetic flux.
A transformer has a primary voltage of 12 V, 50 primary turns, and 250 secondary turns. The secondary voltage is _____ V.
A magnet is moved into a coil twice as fast as before. Compared to the original speed, the induced EMF is:
ApplyBand 3(3 marks) 3. A transformer has 150 turns on the primary coil and 900 turns on the secondary coil, and a primary voltage of 230 V. Calculate (a) the secondary voltage, (b) the turns ratio $N_s : N_p$, and (c) state whether this is a step-up or step-down transformer, and justify your answer.
AnalyseBand 4(3 marks) 4. A bar magnet is dropped, north pole down, through a horizontal copper ring. (a) Explain, using Lenz's Law, why the magnet experiences an upward force as it approaches the ring. (b) Explain why this upward force disappears once the magnet is well below the ring and moving away. (c) Explain, in terms of energy, why the ring warms up slightly during this process.
EvaluateBand 6(4 marks) 5. Induction cooktops, wireless phone chargers, and eddy-current brakes all rely on the same underlying physics as Faraday's 1831 induction ring experiment. Evaluate how these three technologies each apply Faraday's Law and/or Lenz's Law, and explain one key engineering trade-off that must be considered when a changing magnetic field induces unwanted eddy currents in a device's structure, rather than in its intended coil.
Show all answers
Activity 1, Model Answers
- As the north pole approaches, flux into the top of the coil increases. By Lenz's Law, the induced current must create a field opposing this increase, so the top of the coil behaves like a north pole (repelling the approaching magnet). Viewed from above, this means the induced current flows anticlockwise.
- Once the magnet is stationary, the flux through the coil is constant, $\Delta\Phi/\Delta t = 0$, so by Faraday's Law the induced EMF (and current) drops to zero.
- When the magnet is withdrawn, the flux decreases instead of increasing. By Lenz's Law, the induced current reverses direction (now clockwise, viewed from above) to oppose the decrease, trying to maintain the flux.
Activity 2, Model Answers
- $V_s = V_p \times (N_s/N_p) = 240 \times (1000/200) = 1200\ \text{V}$.
- A transformer works by inducing an EMF in the secondary coil from a changing flux, produced by a changing current in the primary. DC produces a constant flux once established, so $\Delta\Phi/\Delta t = 0$ and no EMF is induced in the secondary; AC continuously reverses direction, constantly changing the flux and continuously inducing an EMF.
- The charging pad's coil carries AC, producing a magnetic field that continuously changes direction and magnitude. This changing flux passes through the phone's receiver coil and, by Faraday's Law, induces a current in it, which charges the phone's battery, all without any direct electrical contact.
Short Answer, Model Answers
Q3 (3 marks): (a) $V_s = 230 \times (900/150) = 1380\ \text{V}$. (b) $N_s : N_p = 900 : 150 = 6 : 1$. (c) Step-up transformer, because $N_s > N_p$, so $V_s > V_p$ (the secondary voltage is greater than the primary voltage).
Q4 (3 marks): (a) As the magnet approaches, flux through the ring increases. By Lenz's Law, the induced current creates a field opposing this increase, making the ring's near face effectively the same pole as the approaching magnet, and like poles repel, producing an upward force on the magnet. (b) Once the magnet is well below and moving away, the flux through the ring is decreasing rather than increasing, and (further) once the magnet is far enough away, the rate of flux change becomes negligible, so the induced current, and the opposing force, fades to zero. (c) The induced current flows through the ring's resistance, converting electrical energy into heat ($I^2R$ heating). This energy is drawn from the magnet's gravitational potential energy, which is why the magnet's fall is slower than free fall, energy is conserved overall, just converted from mechanical to thermal form.
Q5 (4 marks): An induction cooktop uses a coil beneath the cooking surface carrying high-frequency AC, producing a rapidly changing magnetic field (Faraday's Law) that induces large eddy currents directly in a ferromagnetic pan, heating it through resistive losses. A wireless phone charger uses a lower-frequency changing field from a coil in the charging pad to induce a current in a small receiver coil inside the phone (Faraday's Law), which charges the battery. An eddy-current brake (used in some trains and roller coasters) moves a conductor through a magnetic field; by Lenz's Law, the induced eddy currents create a field that opposes the conductor's motion, producing a smooth, contact-free braking force without friction or wear. The shared engineering trade-off is that any changing magnetic field will induce eddy currents in any nearby conductor, not just the intended coil. In a transformer, this means eddy currents form in the iron core itself, dissipating energy as unwanted heat and reducing efficiency. Engineers counter this by laminating the core into thin, insulated sheets, which breaks up the possible eddy-current loops (the same principle as the slotted damping plate), trading slightly more complex manufacturing for significantly reduced energy loss.
A full module quiz covering every lesson in this module, not just this one. Set aside a decent block of time and treat it like a real assessment.
Start the module quiz →Michael Faraday, Royal Institution, London, 29 August 1831: two coils on an iron ring, a galvanometer twitched only for an instant when the battery circuit was closed or opened, never while current flowed steadily. That instant of movement is the whole of electromagnetic induction: $\text{EMF} = -N\Delta\Phi/\Delta t$. A magnet dropped through a copper ring falls slower than free fall for exactly this reason, eddy currents induced by the changing flux create a field, by Lenz's Law, that opposes the magnet's own motion.
Now check your Think First answers: a stationary magnet inside a coil induces no EMF at all, the galvanometer reads zero, because the flux is not changing. Pulling the magnet out quickly produces a much larger deflection than pulling it out slowly, same direction, but a far greater rate of change of flux, and therefore a far greater EMF.