Electromagnetic Principles: Flux, Induction, and AC Power Generation

Gauss's Law in Electromagnetism

For a closed surface represented by i, the number of electric field lines leaving the surface is equal to the number of lines entering it. This is consistent with the fact that no net charge is enclosed by the surface. However, for the closed surface ii in the same figure, there is a net outward flux, indicating a net positive charge enclosed.

The situation is radically different for magnetic fields, which are continuous and form closed loops. Examine the Gaussian surfaces represented by i or ii. Both cases visually demonstrate that the number of magnetic field lines leaving the surface is balanced by the number of lines entering it. The net magnetic flux is zero for both surfaces. This is true for any closed surface.

Faraday's Law of Electromagnetic Induction

Faraday’s great insight lay in discovering a simple mathematical relation to explain the series of experiments he carried out on electromagnetic induction. However, before stating and appreciating his laws, we must become familiar with the notion of magnetic flux, Φ_B. Magnetic flux is defined similarly to electric flux, as introduced in Chapter 1.

Magnetic flux (Φ_B) through a plane of area A placed in a uniform magnetic field B (as shown in Figure 6.4) can be written as:

Φ_B = B ⋅ A = BA cos θ

Eddy Currents: Swirling Induced Currents

So far, we have studied electric currents induced in well-defined paths within conductors, such as circular loops. Even when bulk pieces of conductors are subjected to changing magnetic flux, induced currents are produced within them. However, their flow patterns resemble swirling eddies in water. This effect was discovered by the physicist Foucault (1819-1868), and these currents are known as eddy currents.

AC Generators: Harnessing Electromagnetic Induction

The phenomenon of electromagnetic induction has been technologically exploited in numerous ways. An exceptionally important application is the generation of alternating currents (AC). The modern AC generator, with a typical output capacity of 100 MW, is a highly evolved machine. In this section, we will describe the basic principles behind this machine.

The Yugoslav inventor Nikola Tesla is credited with the development of this machine. As pointed out in Section 6.3, one method to induce an electromotive force (EMF) or current in a loop is through a change in the loop’s orientation or a change in its effective area.