PMDC Unit 47 · 4 outcomes

Electromagnetic Induction

Unit 11 is a changing flux making an emf, Lenz’s fight, and transformers — why we send power as high-voltage AC.

11.1

Faraday’s law

PMDC: State Faraday’s law of electromagnetic induction.

A loop sees a changing magnetic flux. An emf appears around the loop. The faster the flux changes, the larger the emf. More turns, more emf. The minus sign in the formula is Lenz (11.2).

Live graph — drag the sliders

ε = - d Φ / d t

$ε$ = − d $Φ$ / dt (one turn)
$ε = - N d Φ / d t (N t u r n s)$
$Φ = B A cos θ$

Hold these

Change B, or A, or the angle — any of those changes $Φ$ and can induce $ε$ .
A steady flux, however large, induces nothing.

11.2

Lenz’s law

PMDC: Account for Lenz’s law to predict the direction of an induced current, and relate it to conservation of energy.

The induced current is in the direction that fights the change. Flux into the loop growing? The loop makes its own field out. Magnet’s N pole approaching? The near face of the coil becomes N and repels.

If it helped the change, you would get energy for free. Lenz is conservation of energy wearing a magnetic coat.

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a pp r o a c hin g \Rightarrow n e a r

face N (repel)

induced current opposes the change in $Φ$

Hold these

Oppose the change, not the field. A falling flux is fought by a current that tries to keep the flux up.
The minus in Faraday’s law is this rule.

11.3

Transformer construction and action

PMDC: Describe the construction of a transformer and explain how it works.

Two coils on a soft-iron core. AC in the primary makes a changing flux in the core. That changing flux threads the secondary and induces an AC emf there. Faraday is the engine. The core couples the two windings and is often laminated to cut eddy-current loss.

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AC primary →

Φ_{c} or e

(t) →

ε_{s} eco n d a r

$V_{s} / V_{p} = N_{s} / N_{p}$
$i d e a l : P_{s} = P_{p} \Rightarrow V_{s} I_{s} = V_{p} I_{p}$
$I_{s} / I_{p} = N_{p} / N_{s}$

Hold these

Needs AC (or any changing current). DC gives one blip, then silence.
More secondary turns: step-up of voltage, step-down of current.

11.4

Step-up, step-down, and the cables

PMDC: Describe how step-up and step-down transformers are used to ensure efficient transfer of electricity along cables.

Power on the line is V I. Loss in the cable is I² R. Raise V, and for the same power you can drop I, so I² R collapses. A step-up transformer at the power station, a long high-V line, a step-down transformer in the town. That is why the grid is AC.

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N_{s} > N_{p} \Rightarrow s t e p - u p V_{s} / V_{p} = 3

$P = V I$
$P_{l oss}$ = I² $R_{c ab l e}$
V × $2 \Rightarrow I /2 \Rightarrow l oss$ / 4 (same P, same R)

Hold these

High V on the pylons, $230 V$ in the kettle.
Step-up then step-down. Both are transformers. Both need AC.

Unit 47 formula sheet

Write these until they are cheaper than thinking, then open the quiz.

$ε$ = − d $Φ$ / dt (one turn)
$ε = - N d Φ / d t (N t u r n s)$
$Φ = B A cos θ$
induced current opposes the change in $Φ$
$V_{s} / V_{p} = N_{s} / N_{p}$
$i d e a l : P_{s} = P_{p} \Rightarrow V_{s} I_{s} = V_{p} I_{p}$
$I_{s} / I_{p} = N_{p} / N_{s}$
$P = V I$
$P_{l oss}$ = I² $R_{c ab l e}$
V × $2 \Rightarrow I /2 \Rightarrow l oss$ / 4 (same P, same R)

Open the Unit 47 quiz