Principles of electromagnetic induction
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Question
Define magnetic flux Φ.
Answer
How much magnetic field threads through a loop: $\Phi = BA\cos\theta$. Unit: **weber (Wb)**.
Question
In Φ = BA cos θ, what is θ measured from?
Answer
The angle between **B** and the **normal** to the loop (not the surface). Square-on ⇒ θ = 0.
Question
When is the flux through a loop zero?
Answer
When the loop is **edge-on** to the field (θ = 90°, cos 90° = 0).
Question
State Faraday's law of induction.
Answer
The induced emf equals the **rate of change** of flux linkage: $\varepsilon = -N\,\Delta\Phi/\Delta t$.
Question
What is needed to induce an emf?
Answer
A **changing** flux. A steady flux — however strong — induces **no** emf.
Question
State Lenz's law.
Answer
An induced current flows so as to **oppose the change** in flux that produced it.
Question
What does the minus sign in Faraday's law mean?
Answer
It is **Lenz's law** — the induced effect opposes the change. This is **conservation of energy**.
Question
Faraday's law vs Lenz's law?
Answer
**Faraday** gives the **size** of the emf; **Lenz** gives its **direction**.
Question
Write the motional-emf formula.
Answer
$\varepsilon = BvL$ — for a rod of length L moving at speed v perpendicular to field B.
Question
Worked: rod L = 0.40 m, v = 3.0 m s⁻¹, B = 0.50 T. emf?
Answer
$\varepsilon = BvL = 0.50\times3.0\times0.40 = 0.60$ V.
Question
Why does a moving rod produce an emf (link to Faraday)?
Answer
As it moves it **sweeps out new area**, so the flux through the circuit changes — that change induces the emf.
Question
How to find the direction of an induced current?
Answer
Apply **Lenz's law**: the current opposes the change in flux (it tries to keep the flux the same).
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Full study notes for Principles of electromagnetic induction
Topic 4.4 hub
Induction (HL)
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