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Induced electromotive force (emf) is a fundamental concept in electromagnetism that explains how voltage is generated in response to a changing magnetic field. Imagine an inductor in a circuit; when the current flowing through it changes, a voltage is induced across the inductor. This induced emf is essential because it acts in a way to oppose the change in current, according to Lenz's law. This opposition helps in stabilizing the current flow within the circuit. The induced emf can be calculated using the formula:

• \(|E| = L |\frac{di}{dt}|\)

This formula tells us that the induced emf (\(E\)) is directly proportional to the product of the self-inductance (\(L\)) and the rate of change of current (\(\frac{di}{dt}\)). In the exercise, we see a real example of using this relationship, where the induced emf is given as 45 V during a change in current of 110 A/s.

An inductor is a passive electrical component capable of storing energy in a magnetic field when electric current flows through it. It typically consists of a coil of wire and is commonly used in electrical circuits to regulate the flow of current or to facilitate energy transfer through magnetic fields.

Inductors are characterized by their inductance, measured in henrys (H), which reflects their ability to induce voltage as current changes. The inductance depends on the number of turns in the coil, the coil’s geometry, and the type of material around which the coil is wound. In circuits, inductors play a crucial role in shaping the behavior of electrical signals, especially in changing and alternating currents. For example, in our exercise, you calculate the self-inductance \(L\) by using the given values of induced emf and the rate of change of current.

The rate of change of current is a vital parameter when dealing with inductors. It refers to how fast the current (\(i\)) is increasing or decreasing over time (\(t\)), and is represented as \(\frac{di}{dt}\). This rate affects the induced emf in an inductor and has practical implications in how circuits respond to varying current conditions.

A steep change in current, or a high \(\frac{di}{dt}\), results in a strong induced emf which can lead to rapidly changing voltages. This relationship is crucial for designing circuits that rely on precise current control, such as filters and oscillators. In our problem, knowing the rate of change of current (110 A/s) was essential to compute the self-inductance, illustrating the direct impact of this concept on practical calculations.