Magnitude of induced emf = rate of change of flux linkage ∆Φ ε = N ∆t…

The idea

The magnitude of an induced emf equals the rate of change of flux linkage, written ε = N ΔΦ/Δt, where N is the number of turns and ΔΦ/Δt is the rate of change of flux through one turn. For a straight conductor of length L moving with speed v perpendicular to a uniform magnetic field B, the emf is ε = BLv because the conductor sweeps area at a rate Lv and cuts flux at that rate. This applies to a rod sliding on rails, a falling conductor or an aircraft wing moving through the Earth’s field. The direction is found from Lenz’s law or the right-hand rule for a moving conductor. If the conductor moves parallel to the field, no flux is cut and the induced emf is zero.

What earns the marks

• The magnitude of the induced emf is the rate of change of flux linkage, ε = N ΔΦ/Δt, with ΔΦ measured in webers and Δt in seconds.
• For a straight conductor of length L moving at speed v perpendicular to a uniform field B, the induced emf is ε = BLv.
• The BLv result follows because the conductor sweeps area at rate Lv, so the rate of change of flux linkage is B × Lv for a single conductor.
• The direction of the induced emf or current is determined by Lenz’s law or by the right-hand rule for a moving conductor.
• If the conductor moves parallel to the magnetic field, it cuts no flux lines and the induced emf is zero.
• Applications include a rod sliding on conducting rails, a conductor falling through a magnetic field and a search coil moving through a field.

Common mistakes and how to put them right

• Using ε = BLv when the conductor moves parallel to the field.

  Put it right: Recognise that no flux is cut and the induced emf is zero.

• Forgetting to include the number of turns N when a coil rather than a single conductor is moving.

  Put it right: Use ε = N ΔΦ/Δt or multiply the single-conductor result by N where appropriate.

• Mixing up the direction rule for a moving conductor with the direction rule for a current-carrying conductor in a field.

  Put it right: Use the moving-conductor rule or Lenz’s law consistently.

Exam tips

• Identify the quantity changing with time before choosing between ε = N ΔΦ/Δt and ε = BLv.
• For a straight conductor, check that the velocity component is perpendicular to the field and use that component in ε = BLv.
• State the direction of the induced current separately from the magnitude calculation, using Lenz’s law or the moving-conductor rule.