20.5 Electromagnetic induction
- Syllabus
- 9702–2028–2029
- Topic
- 20.5
- Level
- A2
Learning objectives
20.5.1Magnetic flux as the product of the magnetic flux density and the• define magnetic flux as the product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density20.5.2Φ = BA• recall and use Φ = BA20.5.3The concept of magnetic flux linkage• understand and use the concept of magnetic flux linkage20.5.4Experiments that demonstrate: • that a changing magnetic flux can induce an• understand and explain experiments that demonstrate: • that a changing magnetic flux can induce an e.m.f. in a circuit • that the induced e.m.f. is in such a direction• As to oppose the change producing it • the factors affecting the magnitude of the induced e.m.f.20.5.5Faraday’s and Lenz’s laws of electromagnetic induction• recall and use Faraday’s and Lenz’s laws of electromagnetic induction
Magnetic flux is field strength multiplied by perpendicular area
Magnetic flux through a surface is Φ=BA cosθ, where θ is the angle between field and the surface normal; units are webers.
Use the component of B perpendicular to the area and state the surface orientation.
A 0.20 T field through 0.50 m² perpendicular surface gives 0.10 Wb.
Flux is not simply B times any projected length, and it is zero when the field lies entirely in the plane of the surface.
Use Φ=BA for a uniform field normal to an area
For a uniform magnetic field perpendicular to a surface of area A, magnetic flux is Φ=BA. The area is the enclosed cross-sectional surface, not wire length or circumference.
1Wb=1Tm2
For B=7.2×10⁻³ T through A=3.2×10⁻⁴ m² normally, Φ=(7.2×10⁻³)(3.2×10⁻⁴)=2.3×10⁻⁶ Wb.
Atnormalangleθ:Φ=BAcosθ.Face−on(θ=0°)givesmaximumBA;edge−on(θ=90°)giveszero.
At fixed orientation, doubling B or A doubles Φ. For a circular loop use A=πr² and convert all lengths to metres before squaring.
Φ=BA without an angle applies only when B is normal to the area. Do not multiply by number of turns here—that produces flux linkage NΦ, not flux through one turn.
Flux linkage counts the total flux through turns of a coil
Flux linkage is NΦ for a coil of N turns when each turn links the same flux; it measures the total linked flux that can induce emf.
Changing turns, field, area or orientation can change linkage. Distinguish flux through one turn from linkage of the whole coil.
A 100-turn coil with 2 mWb per turn has flux linkage 0.20 Wb-turn.
NΦ is not magnetic flux in one turn and does not have the same physical unit interpretation as Φ alone.
Experiments show that changing flux linkage induces an opposing emf
| Magnet–coil action with coil connected to centre-zero galvanometer | Observation | Inference |
|---|---|---|
| magnet stationary relative to coil | zero deflection | static flux gives no induced emf |
| move magnet into coil | transient deflection | changing linkage induces emf/current |
| withdraw same pole | opposite deflection | induced direction reverses to oppose reversed change |
| move faster / use stronger magnet / add turns | larger deflection | larger rate of change of flux linkage gives larger emf |
Place a primary coil connected to a switchable supply beside a secondary coil connected to a galvanometer. Closing or opening the switch gives only a transient secondary deflection; steady primary current gives none. Reversing primary current reverses the induced deflection.
| Change | Why induced emf magnitude increases |
|---|---|
| faster motion/field change | same linkage change in less time |
| stronger B or ferrous core | larger flux change per turn |
| larger coil area / better orientation change | larger change in perpendicular flux |
| more turns N | larger change in total linkage NΦ |
An induced emf exists when linkage changes even if the circuit is open; an induced current requires a complete conducting path.
A magnetic field need not be changing everywhere; what matters is changing flux linkage through the circuit. Lenz's opposition is to the change producing the emf, not automatically to the external field itself.
Use Faraday's law for emf magnitude and Lenz's law for direction
| Law | Statement |
|---|---|
| Faraday | induced emf magnitude is proportional to the rate of change of magnetic flux linkage |
| Lenz | induced emf/current has a direction whose effects oppose the change producing it |
ε=−d(NΦ)/dtForafiniteuniformchange,magnitude∣ε∣=∣Δ(NΦ)∣/Δt=N∣ΔΦ∣/Δt.
If flux per turn of a 200-turn coil changes from 3.0 μWb to 0.50 μWb in 0.010 s, |ε|=200(2.5×10⁻⁶)/0.010=0.050 V.
| Lenz direction step | Action |
|---|---|
| 1 | decide whether external flux through the loop is increasing or decreasing |
| 2 | choose the induced field that opposes that change (oppose increase, support a decrease) |
| 3 | use the right-hand grip rule to convert induced field into conventional current |
| 4 | infer terminal polarity/current direction as requested |
Opposition is required by energy conservation: if induced effects assisted the change, the system could amplify motion and electrical output without external work.
Use change in flux linkage, not final flux alone. The negative sign encodes Lenz direction; it does not mean every voltmeter reading must be numerically negative. An induced field opposes the change, so it may align with the original field when that field is decreasing.