Magnetic Flux Linkage

Oscilloscope: To measure the peak-to-peak voltage of the induced emf.
Large circular coil: Produces a uniform magnetic field.
Stands: To hold the circular coil and search coil in position.
$50$ Hz AC supply: Powers the large coil to create an alternating magnetic field.
Protractor card: For accurately measuring angles.
Search coil: Detects changes in magnetic flux linkage.

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Mount the large circular coil vertically on a stand. Position the search coil at the centre of the circular coil, initially parallel to it. Place the protractor card beneath the coils to measure the angle accurately.
Connect the circular coil to the AC supply and the search coil to the oscilloscope as shown in the diagram.

Turn on the AC supply. Adjust the oscilloscope's voltage sensitivity and time base settings for clear readings. Record the peak-to-peak voltage of the induced AC voltage in the search coil.

Tilt the search coil to change the angle $\theta$ between its plane and that of the circular coil. Increase $\theta$ by $10°$ increments, up to a maximum of $90°$ , using the protractor to measure each angle.
For each angle, record the peak-to-peak voltage displayed on the oscilloscope.

For each angle $\theta$ , calculate $\cos(\theta)$ and tabulate these values alongside the corresponding emf readings.

Plot a graph of induced emf (y-axis) against $\cos(\theta)$ (x-axis). Draw a line of best fit.
The graph should yield a straight line through the origin, demonstrating that the emf in the search coil is proportional to $\cos(\theta)$ .

\varepsilon = BAN \omega \cos(\theta)

This relationship confirms that the induced emf depends on the cosine of the angle between the magnetic field and the plane of the search coil.

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Minimal Risks: This practical has minimal safety concerns, but ensure the setup is stable to avoid accidental movement of the coils.

To accurately read the angle, view the protractor from directly above. Alternatively, use a set square to align the search coil accurately with the protractor.

A data logger with a magnetic field sensor could be used to automatically record the emf, minimising human error.

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Magnetic Flux Linkage: The emf induced in the search coil depends on the rate of change of magnetic flux linkage, which varies with $\cos(\theta)$ .
Relationship to Angle: This experiment verifies that the emf is maximised when the coil is parallel to the magnetic field (i.e., $\theta = 0°$ ) and decreases as the angle increases, reaching zero when the coil is perpendicular to the field ( $\theta = 90°$ ).
Application of Faraday's Law: This practical demonstrates how changing magnetic fields induce emf in a coil, as described by Faraday's Law of Induction.

Magnetic Flux Linkage Simplified Revision Notes for A-Level AQA Physics