Free Pearson Edexcel International A Level Physics lesson
Flux and electromagnetic induction
An induced voltage responds to changing linkage and opposes the change that produces it.
What you’ll learn
- Distinguish B, flux and flux linkage.
- Use Faraday and Lenz laws.
- Explain induction by motion and by changing current.
Count how much magnetic field crosses an area
Magnetic flux through a flat surface in a uniform field is Φ = BA cos θ, where θ is measured between B and the normal to the surface. The normal is perpendicular to the surface, not along it. Flux is greatest when the field passes straight through the area and zero when the field lies in its plane.
Flux has units weber, equivalent to tesla square metre. Flux density B describes field locally; flux describes field through an area. A coil with N identical turns linking the same flux has flux linkage NΦ. Changing the number of turns changes linkage without changing the underlying field or single-turn flux.
Choose a normal direction to assign the sign of flux. Turning a coil through 180° reverses that sign even if B and area magnitudes stay constant. A nonuniform field needs the contributions over small areas to be added; BA assumes a uniform perpendicular component. Distinguishing these quantities prevents confusing a large constant linkage with a large induced voltage.
Φ = BA cos θ; flux linkage = NΦ; 1 Wb = 1 T m²
Symbols and units
- Φ is magnetic flux in Wb
- B is flux density in T
- A is loop area in m²
- θ is angle between B and the area normal
- N is number of turns.
How the equation explains the idea
- Only the field component normal to the loop contributes to flux, so Φ = BA cos θ for a uniform field through a flat loop.
- For N equal turns linking the same flux, total linkage is NΦ. A field in the loop plane has θ = 90° and zero flux; θ is not measured from the plane itself.
Conditions. Uniform B = 0.10 T through a flat loop of area 0.010 m². Angle is measured from the chosen positive area normal. Φ = BA cos θ is converted from Wb to mWb.
Field-to-normal angle / degrees; Signed flux / mWb.
Flux is +1 mWb at 0°, zero at 90°, and −1 mWb at 180°. The negative sign records the field crossing opposite to the chosen normal; the area and field magnitudes remain unchanged.
Open the interactive lesson to view the plotted curves and their coordinate tables.
Worked example
A tilted search coil
- N = 200, A = 3.0 × 10⁻⁴ m² and B = 0.50 T.
- With θ = 60° to the normal, Φ = 0.50 × 3.0 × 10⁻⁴ × 0.5 = 7.5 × 10⁻⁵ Wb.
- NΦ = 0.015 Wb turn.
The cosine uses the angle to the normal, not to the plane.
Keep this idea. Flux crosses an area; linkage adds the flux through the turns.
The slope of linkage gives induced voltage
Faraday’s law states that induced emf magnitude equals the rate of change of flux linkage. A magnet moved quickly into a coil changes linkage more rapidly than the same movement made slowly, producing a larger voltage pulse. More turns or a stronger field can also increase the linkage change for the same motion.
Lenz’s law supplies the sign: the induced effect opposes the change in linked flux. It does not necessarily oppose the original field. When an approaching magnet increases inward flux, the induced current produces opposing flux; when the magnet recedes, the induced current reverses to oppose the decrease. Use this reasoning before applying a hand rule to find a current direction.
On a linkage-against-time graph, the emf is the negative gradient. Constant linkage gives zero emf, while a straight falling segment gives constant positive emf under the chosen orientation. For a finite interval the average emf is −Δ(NΦ)/Δt. A closed circuit is needed for current, but an open coil can still develop an emf across its ends.
ε = −d(NΦ)/dt; average ε = −Δ(NΦ)/Δt
Symbols and units
- ε is induced emf in V
- NΦ is signed flux linkage in Wb turns
- t is time in s
- N is dimensionless turn count.
How the equation explains the idea
- Over a short interval, average emf is minus the linkage change divided by time. The instantaneous value is the negative tangent gradient of linkage against time.
- A linkage increase of 0.060 Wb turns in 0.020 s gives average emf −3.0 V in the chosen loop orientation. The sign expresses opposition to the change, not opposition to every existing magnetic field.
Conditions. Prescribed piecewise-linear linkage through a fixed oriented coil. Linkage rises from 0 to 0.06 Wb turns in 1 s, stays constant for 1 s, then falls to zero over 2 s. Ideal slope jumps occur at the corners.
Time / s; Flux linkage / Wb turns.
From 0–1 s emf is −0.06 V; from 1–2 s it is zero; from 2–4 s it is +0.03 V. Constant nonzero linkage gives no emf. Instantaneous values at ideal sharp corners are not assigned.
Open the interactive lesson to view the plotted curves and their coordinate tables.
Worked example
A coil leaves a field
- Flux linkage falls from 0.024 to 0.004 Wb turn in 0.010 s.
- Δ(NΦ) = −0.020 Wb turn.
- Average ε = −(−0.020)/0.010 = +2.0 V for the stated normal convention.
The sign records opposition to the linkage change.
Keep this idea. Use linkage rate for emf magnitude and opposition to change for its direction.
Changing current can replace moving magnets
A current in one coil creates a magnetic field. If a second coil links part of that field, changing the first current changes the second coil’s flux linkage and induces an emf. No mechanical motion is required. Switching on direct current produces a transient; once the current settles, an ideal stationary secondary has no continuing induced emf.
An alternating current continuously changes the field and can sustain alternating emf in a linked coil. More secondary turns, stronger magnetic coupling and a more rapid primary-current change increase the induced voltage. An iron core can guide more flux through both coils, but leakage and saturation limit a simple proportional model.
For a quantitative graph, use the secondary linkage change rather than assuming it equals the primary linkage. A current ramp gives approximately constant secondary emf when linkage is proportional to primary current. Reversing the ramp reverses the emf. Coil heating, source limitations and core behaviour should be considered when a measured pulse differs from the ideal prediction.
εsecondary = −d(N₂Φlinked)/dt; constant primary current ⇒ constant linked flux ⇒ εsecondary = 0
Symbols and units
- N₂ is secondary turn count
- Φlinked is flux per secondary turn in Wb
- εsecondary is emf in V
- t is time in s.
How the equation explains the idea
- Changing primary current changes its magnetic field and potentially the flux linked by the secondary. The secondary emf depends on the rate of that linked-flux change.
- Once primary direct current is steady and geometry is fixed, linked flux is constant and induced secondary emf is zero. A large steady field alone is insufficient; switch-on and switch-off transients are different.
Worked example
Two linked coils
- Secondary linkage changes from 0.010 to 0.050 Wb turn while primary current ramps for 0.020 s.
- Average εsecondary = −(0.050 − 0.010)/0.020.
- The result is −2.0 V under the defined normal convention.
The induced voltage responds to a changing primary current, not just its nonzero value.
Keep this idea. A changing current induces voltage by changing the field linked to another coil.
Open the interactive lesson for free practice and reviewed three-question samples when available. New full question sets and timed unit checks are in preparation. Existing complete Physics revision packs retain paid access; existing free teaching PDFs remain free.
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