D.4 Induction

UNIT SYLLABUS

HL 6 hours · HL only

Induction is electromagnetism running in reverse: instead of currents making magnetic fields, changing magnetic fields make currents. The bookkeeping quantity is magnetic flux $\Phi = BA\cos\theta$ — count the field lines threading a loop — and Faraday's law says the induced emf equals the rate the flux changes, multiplied by the number of turns. Lenz's law fixes the sign: the induced current always opposes the change creating it, because anything else would be a free-energy machine. Rotate a coil in a field and the flux changes sinusoidally — that single idea is the alternating-current generator, and with it, the entire electrical grid.

Guiding Questions

? How can a changing magnetic field give rise to an electric current?
? Why must the induced effects oppose the changes that produce them?

✓ What the IB expects you to master

Calculate magnetic flux $\Phi = BA\cos\theta$ .
Apply Faraday's law: the induced emf is $\varepsilon = -N\frac{\Delta\Phi}{\Delta t}$ .
Use $\varepsilon = BvL$ for a straight conductor moving perpendicular to a uniform field.
Apply Lenz's law to find the direction of induced currents, and justify it by conservation of energy.
Describe the sinusoidal emf induced in a coil rotating in a uniform field.
Explain how changing the rotation frequency changes both the frequency AND the peak value of the induced emf.

1 Key Formulas

Magnetic flux

\Phi = BA\cos\theta

Faraday's law

\varepsilon = -N\frac{\Delta\Phi}{\Delta t}

Moving conductor

\varepsilon = BvL

2 Exam Preparation & Topic Explanations

Flux first, emf second

Every induction problem starts by writing the flux $\Phi = BA\cos\theta$ and asking which factor changes: $B$ (electromagnets, moving magnets), $A$ (sliding rods, expanding loops) or $\theta$ (rotating coils). The emf is the RATE of that change, times turns.

For generator graphs: emf is maximum when the coil lies IN the plane of the field (flux zero, changing fastest) and zero at the flux maximum — they are 90° out of phase.

Pro Exam Strategy

Emf is induced by CHANGING flux — a huge steady flux induces nothing.
Doubling rotation frequency: peak emf doubles AND period halves. Draw both sinusoids.
$\varepsilon = BvL$ needs mutual perpendicularity of B, v and L — state it.
Direction questions: name Lenz's law, identify the flux change, state the induced pole or current sense that opposes it. Three steps, three marks.

3 MCQ Practice

Q1. A magnet is dropped through a copper ring. As it approaches, the induced current creates a magnetic field that:

Attracts the magnet, speeding it up
Repels the magnet, slowing it down
Has no effect on the magnet
Reverses the polarity of the magnet

Q2. The peak emf of a rotating-coil generator is doubled when the rotation frequency is doubled because:

The flux through the coil doubles
The maximum rate of change of flux doubles
The number of turns effectively doubles
The magnetic field strength doubles

Q3. A conducting rod slides at constant velocity along frictionless rails, completing a circuit in a uniform field. The force needed to keep it moving at constant velocity:

Is zero, since velocity is constant
Equals the magnetic force $BIL$ opposing the motion
Increases with time
Depends only on the rod's mass

4 Short Answer Questions

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