• ### Unit 5: Electromagnetic Induction

We have learned that stationary electric charges produce an electric field, and that moving electric charges (electric current) produce a magnetic field. In this unit, we discover that the reverse is also true: changing magnetic fields can produce an electric field, or induce an electric current. This describes the phenomenon of electromagnetic induction, a basic principle that drives electric power generators and transformers.

Completing this unit should take you approximately 13 hours.

At this point, our discussion of magnetism has been restricted to magnets, currents and wires that do not change over time. Yes, currents involve moving charges, but direct currents (DC) produce constant magnetic fields. Now we will be concerned with magnetic fields that change over time. This can be caused because the source of the magnetic field is itself in motion; or because the strength of that source is changing, which happens in a current-carrying wire if you change the current (for example by connecting it to an AC power outlet).

Faraday's Law of Induction (or Faraday's Law), named after Michael Faraday (1791–1867) an English scientist, refers to the basic law of electromagnetism that predicts how a time-varying magnetic field interacts with an electric circuit to produce an electromotive force (EMF). This phenomenon is known as electromagnetic induction. Magnetic induction provides the foundation for electric motors, generators, transformers, and the electric power grid.

Lenz's Law, named after the Russian physicist Heinrich Lenz (1804–1865), states that introducing a conductor within a magnetic field will produce electricity, inducing an opposing magnetic field that repels the magnetic field producing the charge. Lenz's Law is a consequence of the conservation of energy.

• ### 5.2: Motional Emf

Earlier, we saw that when you move a bar magnet into and out of a conducting loop, an emf is generated inside the loop that will give rise to a circulating current. Another point of view can explain this effect as a consequence of the Lorentz force: just look at things from the perspective of the bar magnet! Such a change of reference frame is always permitted in physics if we assume the bar magnet is approaching at constant velocity.

An electron sitting idly inside the conducting loop will look to the bar magnet as if the electron is approaching, when in actual fact the magnet is approaching the loop. That is, in the frame of reference of the bar magnet the electron represents a moving charge with a velocity that intersects the magnetic field lines of the magnet at some angle. A moving charge will be deflected according to the Lorentz force law. And if this deflection has a component tangential to the loop it will create a current.

The lesson from this change of viewpoint is that induction is all about relative motion. It could be that field lines through a loop are changing because a bar magnet is being moved, or because the loop is being moved. Faraday's Law of induction offers a way to unify many of these effects, giving a single equation that can explain multiple different phenomena where voltages are generated.

• ### 5.3: Eddy Currents

An important part of applying Faraday's Law of induction is to find the correct direction of the emf, and hence the induced current in a conducting loop. To help us with this, we look to a useful rule that only concerns the directions, but not the magnitude of the induction: Lenz's Law. It is based on the fact that any circulating current is itself the source of a magnetic field.

Lenz's Law says that when a current is induced by a changing magnetic flux, the direction in which that current circulates is always such that the magnetic field generated by that circulation itself opposes the change in magnetic flux that is being imposed on the loop.

That is, if the magnetic flux happens to be increasing, the induced current will generate a magnetic field that by itself would create a negative flux. If the magnetic flux happens to be decreasing, the induced current will be directed just right so that it produces a positive magnetic flux.

• ### 5.4: Electric Generators

Electric generators transform mechanical energy into electrical energy, typically by electromagnetic induction via Faraday's Law. For example, a generator may consist of a gasoline engine, attached to a system of coils and/or magnets, which turns a crankshaft.

• ### 5.5: Transformers

As their name implies, transformers change voltages from one value to another – we use the term voltage rather than emf, because transformers have internal resistance. Many cell phones, laptops, video games, and power tools and small appliances have a transformer built into their plug-in unit that transforms 120 V or 240 V AC into the voltage the device uses.

Engineers use transformers at several points in the power distribution systems. Power is sent for long distances at high voltages, because less current is required for a given amount of power, and this means less line loss. Since high voltages can be quite dangerous, we use transformers to produce lower voltage at the user's location.

What makes transformers different from motors and generators is the forms of energy that are involved. Generators transform mechanical to electrical energy; motors transform electrical to mechanical energy – and transformers transform electrical to electrical energy.

• ### 5.6: Electrical Safety

Let's take a moment to review two hazards of electricity. A thermal hazard occurs during electrical overheating. A shock hazard occurs when electric current passes through a person.

• ### 5.7: Inductance

Induction refers to when changing magnetic flux induces an emf. For example, transformers induce a desired voltage and current with little loss of energy. Inductance (or more specifically self-inductance) refers to the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor, and when the magnetic field changes there will be an opposing induced emf according to Faraday's Law. The back emf of a motor is an example of this effect.

• ### 5.8: RC, RL, and RLC Circuits

An RC circuit is a series connection of resistance and capacitance. This circuit stores energy in the form of an electric field. An RL circuit is a series combination of resistance and inductance which stores energy in the form of magnetic energy. An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel.