understand and explain experiments that demonstrate: • that a changing magnetic flux can induce an e.m.f. in a circuit • that the induced e.m.f. is in such a direction as to oppose the change producing it • the factors affecting the magnitude of the

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic flux through a closed conducting circuit produces an electromotive force (e.m.f.) in that circuit. The phenomenon is described by Faraday’s law and Lenz’s law.

Key Concepts

• Magnetic flux, \$\Phi = BA\cos\theta\$, where \$B\$ is magnetic field strength, \$A\$ is the area of the loop, and \$\theta\$ is the angle between \$B\$ and the normal to the loop.
• Faraday’s law: \$\mathcal{E} = -\frac{d\Phi}{dt}\$ where \$\mathcal{E}\$ is the induced e.m.f.
• Lenz’s law: The induced e.m.f. produces a current whose magnetic field opposes the change in flux that produced it (the negative sign in Faraday’s law).

Experiments Demonstrating Electromagnetic Induction

1. Moving a Magnet Into/Out of a Coil

This classic experiment shows that a changing flux induces an e.m.f. and that the direction of the induced e.m.f. opposes the change.

1. Connect a galvanometer (or a sensitive voltmeter) to a single-turn coil.
2. Insert a bar magnet quickly into the coil and observe a deflection on the galvanometer.
3. Withdraw the magnet rapidly; the galvanometer deflects in the opposite direction.
4. Reverse the polarity of the magnet and repeat; the direction of deflection again reverses.

2. Rotating a Coil in a Uniform Magnetic Field (AC Generator)

This set‑up demonstrates continuous induction and the dependence of e.m.f. on the rate of change of flux.

1. Mount a rectangular coil of \$N\$ turns on a shaft so it can rotate at angular speed \$\omega\$.
2. Place the coil between the poles of a horseshoe magnet producing a uniform field \$B\$.
3. Connect the coil leads to a voltmeter or an oscilloscope.
4. Rotate the coil at a constant speed. The voltmeter shows an alternating e.m.f. with peak value \$\mathcal{E}_{\text{max}} = NAB\omega\$ where \$A\$ is the coil area.
5. Reverse the direction of rotation; the polarity of the e.m.f. reverses, confirming Lenz’s law.

3. Falling Magnet Through a Conducting Tube

This experiment illustrates Lenz’s law as a magnetic damping effect.

1. Drop a strong neodymium magnet through a vertical copper tube.
2. Measure the time taken for the magnet to fall using a stopwatch or motion sensor.
3. Compare with the fall time of a non‑magnetic object of similar size.
4. The magnet falls much slower because the changing flux through the tube induces circulating currents (eddy currents) that create a magnetic field opposing the magnet’s motion.

Factors Affecting the Magnitude of the Induced e.m.f.

Summary of Lenz’s Law

For every experiment described, the direction of the induced e.m.f. (and thus the induced current) is such that the magnetic field it creates opposes the original change in flux. This can be predicted using the right‑hand rule for coils:

• Wrap your right hand around the coil so that your fingers follow the direction of the induced current.
• Your thumb then points in the direction of the induced magnetic field.

Key Equations

• Magnetic flux: \$\displaystyle \Phi = BA\cos\theta\$
• Faraday’s law: \$\displaystyle \mathcal{E} = -\frac{d\Phi}{dt}\$
• Peak e.m.f. for a rotating coil: \$\displaystyle \mathcal{E}_{\text{max}} = NAB\omega\$

Typical A‑Level Exam Questions

1. Explain, with reference to Lenz’s law, why a magnet falling through a copper tube experiences a magnetic drag.
2. A coil of 200 turns, area \$5.0\times10^{-3}\,\text{m}^2\$, rotates at \$300\,\text{rev s}^{-1}\$ in a \$0.20\,\text{T}\$ field. Calculate the peak e.m.f.
3. Describe how you could increase the induced e.m.f. in the moving‑magnet experiment without changing the magnet.