A 45-loop coil produces a maximum emf of 65 V as it rotates with an angular speed of 250 rad /

step 1 Hi, here in this given problem, number of loops in the coil of generator, these are 45, maximum

A 45-loop coil produces a maximum emf of 65 V as it rotates...

A 45-loop coil produces a maximum emf of $65 \mathrm{~V}$ as it rotates with an angular speed of $250 \mathrm{rad} / \mathrm{s}$ in a magnetic field with a strength of $2.0 \mathrm{~T}$. What is the area of the coil?

Key Concepts

Coil and Loop Geometry

The geometry of the coil, specifically the number of loops and the area of each loop, directly affects the total magnetic flux linkage and, consequently, the induced emf. In a multi-turn coil, the effect of each individual loop adds up, emphasizing the importance of coil design in applications of electromagnetic induction. This concept is used to calculate the coil’s area when the other parameters are known.

Rotational Motion in Magnetic Fields

When a coil rotates in a magnetic field, the orientation of its area relative to the field changes over time, leading to a periodic change in magnetic flux. This concept is crucial because it explains why the induced emf is sinusoidal and allows the determination of the maximum emf value, which occurs when the rate of change of the flux is greatest. The angular speed of rotation plays a key role in this process.

Faraday's Law of Electromagnetic Induction

This law explains that a changing magnetic flux through a circuit induces an electromotive force (emf) in the circuit. It is the fundamental principle used to relate the motion of a conductor, like a rotating coil, in a magnetic field to the induced emf. In the context of the problem, the law is applied by relating the maximum induced emf to the product of the number of turns, the magnetic field strength, the area of the coil, and the angular speed of rotation.

Magnetic Flux

Magnetic flux quantifies the total magnetic field passing through a given area. It is calculated as the product of the magnetic field strength and the perpendicular area it penetrates. Understanding magnetic flux is essential because the change in flux, as the coil rotates, directly influences the magnitude of the induced emf according to Faraday's law.

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