Induction

Induction describes the generation of an electrical voltage in a conductor due to a change in magnetic flux over time. The change in magnetic flux can be caused in various ways. Figure 1 illustrates induction using a moving conductor in a magnetic field. As in the previous example (Figure ??), a conductor is penetrated by the magnetic field of a permanent magnet, but with the difference that this time no current flows through the conductor. Instead, the ends of the conductor are connected to a voltage measuring device. If the conductor is now moved by an external force, the Lorentz force acts on the electrons in the conductor. The movement causes a charge separation in the conductor. This charge separation is called induction voltage. As long as the conductor or the inducing magnetic field is in motion, a voltage can be read on the measuring device.

In simple terms, the induced voltage can be calculated using equation 1. The magnitude of the induced voltage \(u_{\mathrm {i}}\) depends on the magnetic flux density \(B\), the length of the conductor in the magnetic field \(\ell \), the speed of movement or flux change \(v\), and the number of conductors in the magnetic field \(N\). Since this voltage varies over time, the symbol \(u_{\mathrm {i}}\) is written in lower case. \begin {equation} u_{\mathrm {i}} = B\cdot \ell \cdot v\cdot N \label {GlvereinfachtInduktionsgesetz} \end {equation}

In general, the induced voltage \(u_{\mathrm {i}}\) is the change in magnetic flux \({\mathrm {d}\varPhi }/{\mathrm {d}t}\) over time multiplied by the number of conductors N. This is reflected in the general law of induction (equation 2). The negative sign is due to Lenz’s law, which states that cause and effect always behave in opposite ways.

\begin {equation} u_{\mathrm {i}} = -N\cdot \frac {\mathrm {d}\varPhi }{\mathrm {d}t}\label {GlInduktionsgesetz} \end {equation}