Electromagnetic Induction

The discovery of electromagnetic induction

Michael Faraday discovered the law of induction in 1831. He conducted an experimental procedure in which he connected a battery, a galvanometer, a magnet, and a conducting wire. You can see this in figure 1.

This is what Faraday discovered during his experiment:

• When he disconnected the battery, there was no flow of electric current, and no magnetic flux was induced in the magnet.
• When he closed the switch, a transient current could be observed flowing through the galvanometer. Faraday named this ‘the wave of electricity’.
• When he opened the switch, the measured current quickly spiked to the opposite side of the readings before returning to zero.

In the following months, Faraday continued his experiments, which led him to discover other properties of electromagnetic induction. He observed the same transient currents when he moved a bar magnet quickly through the coil of wires. He also generated direct current (DC) by rotating a copper disk next to the bar magnet with a sliding electrical lead.

Faraday summarised his findings using a concept he named ‘lines of force’. When the switch was initially changed from open to closed, the magnetic flux within the magnetic core increased from zero to the maximum value (which was a constant value). As the flux increased, an induced current on the opposite side was observed. Similarly, when the switch was opened, the magnetic flux in the core would decrease from its constant maximum value back to zero. Hence, a decreasing flux within the core induced an opposite current on the right side.

Faraday’s law of electromagnetic induction

Faraday observed the outcomes of his experiment and expressed his observations mathematically. He noticed that the sudden change in the magnetic flux within the magnet increased from zero to some maximum value. So, when the flux is changed, an induced current on the opposite side is created.

Faraday concluded that a changing magnetic flux in a closed circuit induces an electromotive force or voltage, which is shown in the equation below. In this equation, ε is the electromotive force (measured in volts), Φ is the magnetic flux in a circuit (measured in weber), N is the number of turns of the coil, and t is time (measured in seconds).

\[\varepsilon = N \cdot \frac{\Delta \phi}{\Delta t}\]

From this equation, we can determine the parameters that affect the magnetic field: a stronger magnet (which affects the magnetic flux), more coils (which affects N), and the speed at which the wire moves.

The Maxwell-Faraday equation

The Maxwell-Faraday equation states that a time-changing magnetic field creates a spatially varying electric field and vice versa. You can see the Maxwell-Faraday equation below, where × is a mathematical symbol that stands for the gradient of the electric field E, and B is the magnetic field. Both fields are a function of position r and time t.

\[\bigtriangledown \cdot E = \frac{-\Delta B}{\Delta t}\]

Lenz’s law of electromagnetic induction

Lenz’s law is also expressed mathematically in the equation below. The minus sign is the addition of Lenz’s law to Faraday’s expression to show that the direction of the induced force opposes the changes in the magnetic field.

\[\varepsilon = -N \cdot \frac{\Delta \phi}{\Delta t}\]

Lenz’s right-hand rule

The direction of the induced current can be found using Lenz’s right-hand rule. We extend our fingers so that they are mutually perpendicular to one another. The thumb points to the force (F), the index finger points in the direction of the magnetic field (B), and the middle finger gives the direction of the induced current (I).

Electromagnetic induction and magnetic flux linkage

You can see this in the equation below, where Φ is the magnetic flux (Wb), N is the number of turns, B is the magnetic flux density (T), and A is the cross-sectional area (m²). When we consider the magnetic flux of a coil, the N component is crucial to calculate the magnetic linkage of a coil.

\[\phi N = BAN\]

We calculate the total magnetic linkage by multiplying magnetic flux by the number of turns in a coil. We can ignore the N term when the magnetic flux of a given area is considered.

\[\phi N = BA\]

Applications of electromagnetic induction

Electromagnetic induction is very important as it is a way to generate electricity in a closed circuit. Electromagnetic induction is very useful in electrical generators, transformers, and motors. The most well-known applications of electromagnetic induction are the AC generator, electrical transformer, and magnetic flow meter.