Magnetic flux linkage and coil angle

Practical method

Aim

Investigate how the peak emf induced in a search coil depends on the angle between the coil and an alternating magnetic field.

Variables

Independent variable: angle θ between the coil's normal and the field
Dependent variable: peak induced emf
Control variables: the current in the field coil (frequency and amplitude); position of the search coil.

Apparatus

• Large field coil (or solenoid) on an a.c. supply
• Small search coil on a protractor mount
• Oscilloscope

Method

1. Pass an alternating current through the field coil to produce an alternating field.
2. Place the search coil at the centre with its plane perpendicular to the field (normal parallel to the field, θ = 0).
3. Record the peak emf from the oscilloscope.
4. Rotate the search coil in steps of 15° to 90°, recording the peak emf each time.
5. Plot peak emf against cos θ: a straight line through the origin.

Sample results

Field coil on 50 Hz a.c.

Analysis

Peak emf is proportional to cos θ, because the flux linkage is NBA cos θ and the emf equals its rate of change. The emf is zero when the coil's plane is parallel to the field (θ = 90°).

Uncertainty

Reading the trace peak to ±1 small division (about ±0.04 V on this setting) gives about 2% at θ = 0 but much more near 90°. The protractor reads to ±1°.

Errors and improvements

Risk assessment

Common mistakes

• Measuring θ to the coil's plane instead of its normal (gives sin instead of cos).
• Expecting emf from a steady (d.c.) field.
• Plotting emf against θ.

Worked analysis

At θ = 60°, the predicted peak emf = 2.00 × cos 60° = 1.00 V, matching the measurement.

Common misconception

An emf is induced only when the flux linkage changes; here the alternating current makes the field, and so the flux linkage, change continuously.