College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
Self-induced EMF (electromotive force) is the voltage generated within an inductor due to the changing magnetic field created by the current flowing through the inductor itself. This self-induced voltage opposes any change in the current, as described by Lenz's law, and is a fundamental property of inductors.
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The self-induced EMF is directly proportional to the inductance of the inductor and the rate of change of the current through it.
Self-induced EMF opposes any change in the current, as described by Lenz's law, and this opposition creates a voltage that tends to maintain the current.
Inductors store energy in the form of a magnetic field, and the self-induced EMF is the voltage required to maintain this magnetic field.
The self-induced EMF is the primary mechanism by which inductors can store and release energy, making them useful for various electrical and electronic applications.
The magnitude of the self-induced EMF is determined by the inductor's inductance and the rate of change of the current, which is why inductors are essential components in circuits that involve changing currents.
Review Questions
Explain how the self-induced EMF in an inductor is related to the changing magnetic field and Lenz's law.
The self-induced EMF in an inductor is directly related to the changing magnetic field created by the current flowing through the inductor. As the current changes, it causes the magnetic field to change, and according to Lenz's law, the self-induced EMF will oppose this change. The self-induced EMF creates a voltage that tends to maintain the current, as the changing magnetic field induces a voltage that opposes the change. This relationship between the self-induced EMF, the changing magnetic field, and Lenz's law is a fundamental principle of inductors and their behavior in electrical circuits.
Describe how the self-induced EMF allows inductors to store and release energy.
Inductors store energy in the form of a magnetic field, and the self-induced EMF is the voltage required to maintain this magnetic field. When the current through an inductor changes, the self-induced EMF opposes this change, creating a voltage that tends to maintain the current. This allows the inductor to store energy in the magnetic field when the current is increasing, and release that energy when the current is decreasing. The self-induced EMF is the key mechanism that enables inductors to act as energy storage devices, making them useful in various electrical and electronic applications, such as power supplies, filters, and timing circuits.
Analyze how the magnitude of the self-induced EMF in an inductor is determined by the inductor's inductance and the rate of change of the current, and explain the significance of this relationship.
The magnitude of the self-induced EMF in an inductor is directly proportional to the inductor's inductance and the rate of change of the current flowing through it. This relationship is expressed by the formula: $$ \varepsilon_\text{self} = -L \frac{di}{dt} $$, where $\varepsilon_\text{self}$ is the self-induced EMF, $L$ is the inductance, and $\frac{di}{dt}$ is the rate of change of the current. The significance of this relationship is that it allows the self-induced EMF to be precisely controlled and utilized in various electrical and electronic applications. The inductance of the inductor, which is a constant property, and the rate of change of the current, which can be manipulated, together determine the magnitude of the self-induced EMF. This understanding is crucial for designing and analyzing circuits that involve inductors and changing currents, as the self-induced EMF plays a crucial role in the behavior and performance of these circuits.