A search coil measures magnetic flux density using Faraday's law

Electromagnetic Induction — AQA A-Level Physics

Key Definition

Search coil — A small coil of known area and known number of turns, used with a voltmeter or oscilloscope to measure magnetic flux density by exploiting Faraday's law.

The search coil is placed inside the magnetic field you want to measure, oriented so the plane of the coil is perpendicular to the field (maximum flux linkageThe product of magnetic flux and the number of turns of a coil. Measured in weberThe SI unit of magnetic flux. One weber is the flux through an area of 1 m² when the magnetic flux density is 1 T perpendicular to the area.-turns (Wb turns).).
To induce an EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V)., you change the flux linkageThe product of magnetic flux and the number of turns of a coil. Measured in weberThe SI unit of magnetic flux. One weber is the flux through an area of 1 m² when the magnetic flux density is 1 T perpendicular to the area.-turns (Wb turns). through the coil. Two common methods: pull the coil quickly out of the field, or rotate it 90° so the flux through it drops to zero.
Measure the induced EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). (either peak value with an oscilloscope, or average value for a quick pull).
Rearrange Faraday's lawThe magnitude of the induced EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). is proportional to the rate of change of magnetic flux linkageThe product of magnetic flux and the number of turns of a coil. Measured in weberThe SI unit of magnetic flux. One weber is the flux through an area of 1 m² when the magnetic flux density is 1 T perpendicular to the area.-turns (Wb turns).. to find B. For the quick-pull method, the initial flux linkage is BAN and the final is zero, so:

\varepsilon_{\text{avg}} = \frac{BAN}{\Delta t}

Rearranging: $B = \varepsilon_{\text{avg}} \times \Delta t / (AN)$, where A is the coil area and N is the number of turns.
For a rotating search coil in a sinusoidal field, connect it to an oscilloscope. The peak EMF reading gives $\varepsilon_{0} = BAN\omega$, from which $B = \varepsilon_{0} / (AN\omega)$.
The coil must be small enough that B is approximately uniform across its area. If B varies significantly across the coil, the measurement gives an average over the coil area.

Common Mistake MEDIUM

Students often: Forgetting that the search coil must have its plane perpendicular to the field (so the normal to the coil is parallel to B) before pulling it out.
Instead: If the coil starts at an angle, the initial flux linkage isn't BAN. You need the coil face-on to the field for the full flux to thread through it, giving the maximum and most accurate reading.