A generator has a 55-loop coil with an area of 0.0085 m^2. If the coil rotates with an angular

step 1 Hi, here in this given problem, number of loops in the generator, this is n is equal to 55 area

A generator has a 55-loop coil with an area of 0.0085 m^2....

A generator has a 55-loop coil with an area of $0.0085 \mathrm{~m}^{2}$. If the coil rotates with an angular speed of $310 \mathrm{rad} / \mathrm{s}$ in a magnetic field with a magnitude of $0.95 \mathrm{~T}$, what is the maximum emf?

Key Concepts

Faraday's Law of Electromagnetic Induction

This law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in the circuit. It forms the foundational principle behind the operation of generators, explaining how mechanical motion in a magnetic field can be converted into electrical energy by means of changing magnetic flux.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. In the context of electromagnetic induction, it is defined as the product of the magnetic field strength, the area through which the field lines pass, and the cosine of the angle between the field direction and the normal to the area. Changes in magnetic flux over time result in induced voltage.

Rotating Coil in a Magnetic Field

A rotating coil in a magnetic field experiences a continuously changing orientation with respect to the magnetic field lines, leading to a sinusoidally varying magnetic flux. This rotation, characterized by the angular velocity, directly affects how rapidly the magnetic flux changes, and hence, determines the magnitude of the induced emf.

Coil Loop Multiplication Factor

The total induced emf in a coil is amplified by the number of loops or turns in the coil. Each loop contributes to the overall voltage, so a greater number of loops results in a higher total induced emf, which is crucial in design and optimization of electromagnetic generators.

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