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Define magnetic flux Φ.
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All Flashcards in Topic 4.4
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4.4.112 cards
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).
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.
Define the rms value of an AC.
The **steady DC value** that delivers the **same average power** (same heating) as the AC.
Convert peak to rms (sine wave)?
$V_{rms} = \dfrac{V_0}{\sqrt{2}}$ and $I_{rms} = \dfrac{I_0}{\sqrt{2}}$ — divide the peak by √2 (≈ 1.41).
Is rms larger or smaller than the peak?
**Smaller** — rms = peak ÷ √2. The mains "230 V" is an **rms** value.
What does a transformer do?
Changes an **AC voltage** up or down using two coils on a shared iron core.
Transformer voltage and turns relationship?
$\dfrac{\varepsilon_p}{\varepsilon_s} = \dfrac{N_p}{N_s}$ — the **voltage ratio equals the turns ratio**.
Step-up vs step-down transformer?
**Step-up**: more secondary turns ⇒ higher V, lower I. **Step-down**: fewer secondary turns ⇒ lower V, higher I.
What does an ideal transformer conserve?
**Power**: $\varepsilon_p I_p = \varepsilon_s I_s$. That is why the **current ratio is inverted**.
Find the secondary voltage of a transformer?
$V_s = V_p \times \dfrac{N_s}{N_p}$ — multiply the primary voltage by the turns ratio.
Topic 4.4 study notes
Full notes & explanations for Induction (HL)
Physics exam skills
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