D.4 InductionIB Physics HL: Revision notes
Section 1
Magnetic flux and flux linkage
The magnetic flux Φ through an area A in a uniform field B is Φ = BA cos θ, where θ is the angle between the field and the normal to the area. Unit: weber (Wb = T m²). Flux is greatest when the field is perpendicular to the plane of the coil (θ = 0) and zero when the field lies in its plane (θ = 90°). For a coil of N turns, the flux linkage is NΦ.
θ is measured from the normal to the coil, not from its plane. If a question gives the angle between B and the plane, use sin, or convert to the angle with the normal.
Section 2
Faraday's law of induction
A time-changing magnetic flux induces an emf: ε = −N ΔΦ/Δt. The flux can change because B changes, the area changes, or the angle changes (rotation). The size of the emf depends on the rate of change of flux linkage, not the flux itself.
Section 3
A conductor moving through a field
A straight conductor of length L moving at speed v perpendicular to a uniform field B has an induced emf ε = BvL. This follows from Faraday's law, because the conductor sweeps out an area vL per second. If the circuit is complete, a current flows and the rod feels a force BIL opposing its motion; the power supplied to keep it moving, Fv, equals the electrical power I²R.
Section 4
Lenz's law and energy conservation
Lenz's law: the induced emf is in a direction such that any induced current opposes the change that produced it. The minus sign in Faraday's law expresses this.
It is a consequence of conservation of energy: if the induced current helped the change, the motion would speed up and generate more current without any energy input. Instead, work must be done against the opposing force, and this work becomes electrical energy (and then internal energy in resistances). Eddy currents in conductors produce magnetic braking in the same way.
For direction questions: first say whether the flux is increasing or decreasing, then state that the induced field opposes that change.
Section 5
The rotating coil (AC generator)
A coil rotating at constant angular speed in a uniform field has Φ = BA cos ωt, which changes sinusoidally, so the induced emf is sinusoidal.
- Emf is zero when the coil's plane is perpendicular to B (flux maximum, not changing).
- Emf is maximum when the plane is parallel to B (flux zero, changing fastest).
Section 6
Changing the frequency of rotation
Increasing the rotation frequency f makes the flux change faster, so:
- the peak emf increases in proportion to f (doubling f doubles the peak emf);
- the period of the emf, T = 1/f, decreases (doubling f halves the period).
The waveform stays sinusoidal.
Doubling the rotation frequency changes BOTH the peak emf and the period, not just one of them.
That's the notes covered.
Carry on to the next subtopic.