Induction (HL)
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Define magnetic flux Φ.
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All Flashcards in Topic 4.4
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Define magnetic flux Φ.
How much magnetic field threads through a loop: $\Phi = BA\cos\theta$. Unit: **weber (Wb)**.
In Φ = BA cos θ, what is θ measured from?
The angle between **B** and the **normal** to the loop (not the surface). Square-on ⇒ θ = 0.
When is the flux through a loop zero?
When the loop is **edge-on** to the field (θ = 90°, cos 90° = 0).
State Faraday's law of induction.
The induced emf equals the **rate of change** of flux linkage: $\varepsilon = -N\,\Delta\Phi/\Delta t$.
What is needed to induce an emf?
A **changing** flux. A steady flux — however strong — induces **no** emf.
State Lenz's law.
An induced current flows so as to **oppose the change** in flux that produced it.
What does the minus sign in Faraday's law mean?
It is **Lenz's law** — the induced effect opposes the change. This is **conservation of energy**.
Faraday's law vs Lenz's law?
**Faraday** gives the **size** of the emf; **Lenz** gives its **direction**.
Write the motional-emf formula.
$\varepsilon = BvL$ — for a rod of length L moving at speed v perpendicular to field B.
Worked: rod L = 0.40 m, v = 3.0 m s⁻¹, B = 0.50 T. emf?
$\varepsilon = BvL = 0.50\times3.0\times0.40 = 0.60$ V.
Why does a moving rod produce an emf (link to Faraday)?
As it moves it **sweeps out new area**, so the flux through the circuit changes — that change induces the emf.
How to find the direction of an induced current?
Apply **Lenz's law**: the current opposes the change in flux (it tries to keep the flux the same).
A magnet's N pole is pushed into a coil. What pole forms at the near end of the coil, and why?
A **N pole**: it repels the magnet, opposing the change (Lenz's law). Pull it out and the near end becomes S.
A loop moves at steady speed into, through and out of a field region. What does its emf do?
Steady while entering, **zero** while fully inside (flux constant), steady and **opposite** while leaving.
How do you get the emf from a graph of flux against time?
emf = **N × gradient**; biggest where the graph is steepest, zero where it is flat.
4.4.212 cards
How does an AC generator work?
A **coil is spun** in a magnetic field. The changing flux induces a **sinusoidal emf** — alternating current (AC).
When is the generator emf at its peak?
When the coil is **edge-on** to the field — the flux is changing **fastest** there.
Peak emf of an AC generator?
$\varepsilon_0 = BAN\omega$ — increase any of **B**, **A**, **N** or **ω** to raise it.
What does B, A, N, ω each stand for in ε₀ = BANω?
**B** flux density, **A** coil area, **N** turns, **ω** angular frequency of rotation.
What happens to a generator's emf if the coil turns twice as fast?
The **peak doubles** (ε₀ = BANω) and the **period halves** (T = 2π/ω).
At which coil position is a generator's emf zero?
When the coil **faces** the field: the flux is largest but momentarily not changing.
How are the flux and emf graphs of a rotating coil related?
Both are sine curves a **quarter turn out of step**: emf largest when the flux is zero.
Why is a generator harder to turn when it supplies a current?
The induced current opposes the rotation (**Lenz**); the work done becomes the electrical energy delivered.
Which changes alter only the peak emf of a generator, not its period?
A stronger field **B**, a larger area **A** or more turns **N**.
How do you find the average emf as a coil turns through part of a revolution?
ε = NΔΦ/Δt with Φ = BA cos θ at the start and the end; a half turn gives ΔΦ = 2BA.
What is the period of a generator's emf?
The time for one turn of the coil: **T = 2π/ω**.
Why is the emf of a rotating coil sinusoidal?
The flux is Φ = BA cos ωt; its **rate of change** follows a sine curve, so the emf does too.
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