Required practicals › Flux linkage and a search coil

REQUIRED PRACTICAL 11

Flux linkage and a search coil

Using a search coil and an oscilloscope to see how magnetic flux linkage varies with the angle between the coil and the field.

Theory: Magnetic flux and flux linkage

What you are trying to do

Use a search coil and an oscilloscope to show that the flux linkage through a coil follows the cosine of the angle between the coil's normal and the field.

Apparatus

  • A large field coil driven by an ac signal generator, producing an alternating field of fixed amplitude at its centre
  • A small search coil of many turns on an insulating handle, mounted on a protractor so its angle can be set
  • An oscilloscope to read the amplitude of the induced emf

Variables

  • Independent: the angle θ between the search coil's normal and the field
  • Dependent: the amplitude of the induced emf on the oscilloscope
  • Control: the field amplitude and frequency, and the search coil's position at the centre of the field coil

Method

  1. Drive the field coil with a steady ac signal; the alternating field induces an emf in the search coil whose amplitude is proportional to its flux linkage.
Tilt the coil and only the component of B along the coil's normal counts: flux linkage N phi = BAN cos theta, with theta measured to the normalnormalθNΦ = BAN cos θθ is to thenormal, notthe coil face
FIG. 1The angle that matters is measured from the field to the coil's NORMAL, not to its face; face-on means θ = 0 and maximum linkage.
  1. Centre the search coil where the field is uniform, set θ = 0 (coil face-on), and record the peak-to-peak height of the trace.
  2. Rotate in steps of fifteen degrees to ninety, recording the amplitude at each angle without moving the coil's centre.
Magnetic flux counts the field passing through an area: face-on to the field, phi equals B times ABarea A, face-on to the fieldΦ = BA, measured in webers
FIG. 2What is being sampled: the flux through the coil's area, scaled by the cosine as the coil turns.

Analysis

  1. The linkage is NΦ = BANcos θ, and the induced amplitude is proportional to it, so plot the amplitude against cos θ.
  2. A straight line through the origin is the result: linkage, and with it the induced emf, follows the cosine of the angle to the normal.

A worked set of readings

Amplitudes from the oscilloscope at fifteen-degree steps:

θ / °cos θAmplitude / V
01.0004.00
150.9663.86
300.8663.46
450.7072.83
600.5002.00
750.2591.04
900.0000.00

Amplitude against cos θ is a straight line through the origin with gradient 4.00 V, the face-on amplitude: linkage follows BANcos θ exactly as the model says.

Where the uncertainty comes from

  • Angle setting: A protractor mount reads to a degree or two; the cosine is flattest near zero, so errors there matter least, and most near ninety degrees.
  • Position drift: The field is uniform only near the centre of the field coil; rotating without translating is the manual skill.
  • Reading the trace: Use peak-to-peak and halve it: the full height is easier to judge against the graticule than a single peak.
  • Amplifier and coupling: Keep the oscilloscope settings fixed for the whole run so every amplitude is on the same scale.

What earns the marks

  • Define θ to the normal, and say face-on is maximum. The angle definition is the most reliably examined sentence in this practical.
  • Plot against cos θ to linearise, and expect the through-origin check.
  • Peak-to-peak halved, with the scope's volts-per-division stated.
  • Know why an ac field is needed at all: a steady flux linkage induces nothing; it is the changing flux that drives the emf.

Safety

Nothing here bites: signal-level voltages throughout. The field coil can warm with sustained drive, so switch off between runs.

Method and analysis here follow the standard approach; your school may vary the apparatus. Always follow your teacher’s risk assessment in the lab.