The armature of a small generator consists of a flat, square...

The armature of a small generator consists of a flat, square coil with 120 turns and sides with a length of $1.60 \mathrm{~cm} .$ The coil rotates in a magnetic field of $0.0750 \mathrm{~T}$. What is the angular speed of the coil if the maximum emf produced is $24.0 \mathrm{mV} ?$

Key Concepts

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic field produces an electric current in a conductor. This principle is fundamental to the operation of generators, motors, and many other electrical devices, and is governed by the rate at which magnetic flux changes through a circuit.

Faraday's Law of Induction

Faraday's Law states that the induced electromotive force (emf) in a circuit is proportional to the rate of change of the magnetic flux through the circuit. This law forms the basis for the mathematical relationship used to calculate the peak emf in rotating coils and other dynamic systems within magnetic fields.

Magnetic Flux

Magnetic flux represents the amount of magnetic field passing through a given area, and its variation is what ultimately leads to the generation of an electromotive force. Understanding magnetic flux is essential for analyzing how changing orientations or variations in the magnetic field intensity can induce a current in a loop or coil.

Rotational Motion in Magnetic Fields

When a coil rotates in a magnetic field, its orientation relative to the field changes continuously, leading to a periodic change in magnetic flux. This rotation, described by its angular speed, directly affects the rate at which the magnetic flux varies, thereby determining the magnitude of the induced emf.

Angular Speed

Angular speed is a measure of how quickly an object rotates, typically expressed in radians per second. In the context of electromagnetic induction in rotating systems, it quantifies the rate of change of the orientation of the coil relative to the magnetic field, influencing the amplitude of the induced emf.

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