Required Practicals / AQA / Practical 11
11 A2 3.7.5.4

Magnetic flux linkage and a search coil

Investigate how the peak EMF induced in a search coil varies with its orientation in an alternating magnetic field.

Apparatus

  • Helmholtz coils or solenoid connected to an AC signal generator
  • Search coil (known number of turns N and area A)
  • Oscilloscope
  • Protractor
  • Connecting leads

Safety

  • Use a signal generator operating within safe low-voltage limits; mains voltage is not required.
  • Ensure the search coil is not mechanically damaged by excessive rotation or tension on the leads.

Method

  1. Connect the Helmholtz coils to the signal generator at a fixed frequency f. Place the search coil inside the field.
  2. Connect the search coil to the oscilloscope input. Read the peak EMF from the oscilloscope trace.
  3. Rotate the search coil to different angles theta between the coil normal and the field direction. Record peak EMF at each angle.
  4. Plot peak EMF against cos(theta): expect a straight line through the origin.
  5. Repeat at a different signal generator frequency to confirm the dependence on omega.

Key Variables

Independent Angle theta between coil normal and magnetic field
Dependent Peak EMF induced in search coil
Controlled Field strength (constant current and frequency in Helmholtz coils); Search coil dimensions

Analysis and Results

  • Flux linkage: $N\Phi = NBA\cos\theta$.
  • Peak EMF $= NBA\omega\cos\theta$ (stationary coil in AC field).
  • Plot peak EMF vs $\cos\theta$: straight line through origin, gradient $= NBA\omega$.
  • Hence $B = \text{gradient}/(NA\omega)$ where $\omega = 2\pi f$.

Common Errors

  • Reading peak-to-peak voltage from the oscilloscope instead of peak voltage (divide peak-to-peak by 2).
  • Defining theta from the plane of the coil rather than the normal to the coil.
  • Using a DC field (constant B gives zero EMF in a stationary coil since $d\Phi/dt = 0$).
  • Allowing the search coil to drift in position between readings, changing its effective area in the field.

Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.

Q1 3 marks

A search coil has 50 turns and area $4.0$ cm$^2$. It is placed at 60 degrees to a magnetic field ($B = 0.025$ T) oscillating at 50 Hz. Calculate the peak EMF.

Q2 3 marks

Explain why an AC magnetic field is used rather than a DC field in this experiment.

Q3 2 marks

The gradient of a peak EMF against $\cos\theta$ graph is 0.50 V. The search coil has 80 turns, area $2.0$ cm$^2$, and the field oscillates at 100 Hz. Calculate B.