Electromagnetic induction flashcards

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Magnetic flux φ
φ = BA: flux density × area at right angles to the field. Unit the weber, 1 Wb = 1 T m².
Flux linkage
Nφ: the flux through one turn multiplied by the number of turns N. Unit Wb (Wb-turns).
Faraday's law
The magnitude of the induced e.m.f. equals the rate of change of flux linkage.
Lenz's law
The induced e.m.f. is in a direction such that any current it drives opposes the change that produced it.
Eddy currents
Loops of current induced inside a solid conductor by a changing flux (or by motion through a field).
Electromagnetic induction
The production of an e.m.f. in a conductor when the flux linking it changes, or when it cuts magnetic field lines.
Transformer (what it is)
Two coils on a shared iron core: an alternating current in the primary induces an alternating e.m.f. in the secondary.
Faraday's and Lenz's laws as an equation
ε = −d(Nφ)/dt; the minus sign is Lenz's law. (Yes)
Average e.m.f. over a time interval
ε = −Δ(Nφ)/Δt. (No — derive it)
E.m.f. in a straight rod moving across a field
ε = Blv, with B, l and v mutually at right angles. (No — derive it)
Flux linkage of a coil face-on to a uniform field
Nφ = NBA. (No — learn it)
Unit equivalences for the weber
1 Wb = 1 T m² = 1 V s. (No — learn it)
How do you get e.m.f. from a flux-linkage–time graph?
ε = minus the gradient (use a tangent for a curve).
Area under an e.m.f.–time graph
Minus the change in flux linkage over that time.
Flat section of a flux-linkage–time graph
Flux linkage not changing, so e.m.f. = 0.
E.m.f.–time graph for a magnet falling through a coil
Two pulses of opposite sign; the second taller and narrower (magnet faster on leaving); e.m.f. = 0 as the magnet passes the centre.
Flux linkage and e.m.f. of a coil rotating steadily in a uniform field
Flux linkage varies as a cosine, e.m.f. as a sine: e.m.f. is zero when flux linkage is maximum and maximum when it is zero.
Secondary e.m.f. when the primary is switched on, left on, then off
A pulse at switch-on, zero while the current is steady, a pulse in the opposite direction (usually larger) at switch-off.
Factors that increase the e.m.f. when a magnet moves relative to a coil
Faster relative motion, stronger magnet, more turns, larger coil area (if the field is wide enough to fill it).
Why does a magnet held still inside a coil induce no e.m.f.?
The flux linkage is large but not changing; e.m.f. depends on the rate of change.
Why won't a transformer work on steady d.c.?
A steady current gives a constant flux, so the secondary's flux linkage does not change and no e.m.f. is induced.
Factors that increase the e.m.f. induced in a secondary coil
Faster change of primary current, more turns, an iron core linking the coils, coils closer together.
Why is Lenz's law a consequence of energy conservation?
If the induced current aided the change, energy would be created from nothing; opposing it means work must be done to produce the electrical energy.
How does magnetic braking work?
Motion through the field induces eddy currents in the conductor; by Lenz's law they produce a force opposing the motion, and kinetic energy becomes thermal energy.
Why does a magnet fall slowly down a copper tube?
Eddy currents in the tube oppose its motion; the braking force rises with speed until it equals the weight: terminal velocity.
Why are transformer cores laminated?
Insulated thin sheets break up eddy-current loops, reducing energy wasted as heat in the core.
Flux through each of 300 turns falls steadily from 2.0 × 10⁻⁴ Wb to zero in 0.050 s. E.m.f.?
Δ(Nφ) = 300 × 2.0 × 10⁻⁴ = 0.060 Wb; ε = 0.060 / 0.050 = 1.2 V. (Yes)
A 0.50 m rod moves at 5.0 m s⁻¹ at right angles to a 0.080 T field. E.m.f.?
ε = Blv = 0.080 × 0.50 × 5.0 = 0.20 V.
Flux linkage falls in a straight line from 0.024 Wb to zero in 60 ms. E.m.f.?
ε = −gradient = −(0 − 0.024) / 0.060 = +0.40 V.
Coil: 100 turns, 3.0 × 10⁻³ m², in 0.20 T, rotating at 50 rev s⁻¹. Average e.m.f. from face-on to edge-on?
NBA = 0.060 Wb; quarter turn = 0.020 / 4 = 0.0050 s; ε = 0.060 / 0.0050 = 12 V.
The rod in the 0.20 V example is part of a 0.40 Ω circuit. Current and opposing force?
I = 0.20 / 0.40 = 0.50 A; F = BIl = 0.080 × 0.50 × 0.50 = 0.020 N.
Forgetting N
Faraday's law uses flux linkage Nφ; using φ alone gives an answer N times too small.
Area in cm²
Convert to m² before calculating flux: 1 cm² = 1 × 10⁻⁴ m².
Direction questions on Lenz's law
State what is changing, then that the induced current opposes it, then the direction or pole.
E.m.f. when flux linkage passes through zero on a straight line
Not zero: the gradient is unchanged, so the e.m.f. is the same as on the rest of the line.
Rotating coil: where is the e.m.f. largest?
Edge-on to the field (flux linkage zero), not face-on.
E.m.f. versus current
An e.m.f. is induced whenever flux linkage changes; a current flows only if the circuit is complete.

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